Some years ago, I had the idea of grading science fiction according to the degree of scientific realism. It was very obvious to me that, for example, the Discovery One spaceship in 2001 A Space Odyssey was far more realistic than the Star Destroyers, X-Wings, and Tie-Fighters of Star Wars.
There's actually a name for scientifically rigorous science fiction. Hard Science Fiction, or Hard SF for short, is so called because it focuses on scientific veracity and the "hard" sciences like physics and astronomy. Back in the 1940s, writers like Asimov, Clarke, and Heinlein revolutionised Science Fiction and helped define the field by referencing real science and logic in place of the early "pulp" stories, although the actual term "Hard Science Fiction" only appeared later.
There is, however, no official term for the opposite of Hard SF. There is "Soft Science Fiction," but this refers to science fiction based on the "soft" sciences like sociology, anthropology, and psychology. It's not that Soft SF is less realistic so much as it has different standards of realism, such as different cultural possibilities instead of different planets (which is more typical of Hard SF). Ursula Le Guin is the most influential representative of this sociological approach to science fiction. I don't focus on classic Soft Science Fiction here not because it isn't any good, but because it's a genre I have not read much of.
Hard SF and Social Science Fiction are only two of many sub-genres of Science Fiction. Others include space opera, planetary romance, military SF, soft science fiction, new wave, alternative history, cyberpunk, post-apocalyptic, science fantasy, dystopia, steampunk, and so on. So while some science fiction stories are indeed rigorous when it comes to physics or rocket science, they are actually only a small minority of the overall genre of science fiction.
Someone, I don't know who, came up with the idea of using the mineralogy, specifically the Mohs Scale of Hardness, which determines the hardness of minerals through the harder mineral being able to scratch the softer one. This since became a humorous metaphor for realism (Hard SF) or lack thereof in science fiction. In this context, "soft scifi" has nothing to do with literary science fiction, but refers to movies like Star Wars which has things like spaceships wheeling and banking in a vacuum (which wouldn't work because a vacuum, unlike air, has no friction).
A perfect scale of science fiction hardness would have a quantitative list of dos and don'ts by which a movie or story can be assessed; the more scientifically accurate the story, the harder the hard SF; the more ridiculousness in the story, the opposite. Scientific absurdities would include things like: human-like aliens, explosions and fireballs causing shockwaves in a vacuum, "down" being perpendicular to direction of travel, unlimited thrust from rocket engines, landing on a convenient nearby planet to make repairs, causing a computer or AI to self-destruct by giving it a problem it can't solve logically, giant mecha or monsters that don't collapse under their own weight, lifeless planets with breathable air, and so on.
Tropes that go against everything we currently know about how the universe works but that can be justified as plot devices by imagined future discoveries include: forcefields, faster-than-light travel, antigravity, materials strong enough to build rotating rings or structures that are millions of kilometers in diameter. Scientific authenticity would include things like: spacecraft having thermal radiators, spacecraft and habitats requiring shielding against cosmic radiation, ion and fusion rockets only having small thrust, conservation of energy, most worlds being hostile environments, and so on. I haven't bothered to add up all these things in any sort of quantitative analysis here (which is why the following scale is only half serious), but it could be a project for someone with a lot of time to waste.
Of course, just because someone gets the science right doesn't mean the story is amazing. Too much obsession with authenticity can easily get in the way of telling a good story by limiting the imagination. So these ratings are not meant as a derogatory (soft scifi) versus elitist (hard SF) assessment, rather simply as an entertaining and perhaps pointless meditation. The examples I provide for each 'level' are not meant to be definitive, but simply fun suggestions; you may grade these differently (as well as add others I've left out). Also, as my own preferred genre is in space-based science fiction, these examples predominate my list, and a great many other science fiction writers are therefore not mentioned.
So without further ado, here is my somewhat debatable Scale of Science Fiction Hardness.
0. Cartoons. These are simply for kids' entertainment; they are not meant to make sense and offer no explanation of anything, e.g. Marvin the Martian.
1. Superhero Fiction and equivalent. All superheroes break the laws of physics in numerous ways and hence are totally unscientific. Even token attempts at explanations are scientifically nonsensical: e.g. Superman gets his powers because the Earth has a yellow (brighter) rather than a red (dimmer) sun, and the Earth's gravity is lighter than that of Krypton; the X-Men have genetic mutations. In addition to the DC and Marvel superhero universes there is also completely impossible manga and anime, like Dragonball Z (superpowered martial arts), and mecha bigger than galaxies in Tengen Toppa Gurren Lagann.
2. SciFi and Science Fantasy. The term "Scifi" is generally used to refer to science fiction movies and popular culture, as opposed to "SF" which refers to purely literary science fiction. It follows that "SciFi" will almost always be less realistic, because of the need to use human actors with only cosmetic makeup as aliens, the difficulty of producers investing millions in complex concepts that will be over most viewers' heads, and other such reasons. Hence Hollywood (and other movie and TV) science fiction, and all other popular scifi works are based on what looks good artistically (and hence what can be marketed) rather than what is realistic. Ships wheel and bank in a vacuum, laser bolts move at the speed of tracer rounds, stormtroopers can't shoot straight, aliens are usually similar or identical to H. sapiens, eat same food, speak English, and so on. There may also be giant monsters or giant robots which would, in real life, be impossible because of the effects of gravity (as height doubles, weight increases eight times; this is known as the Square Cube Law, which is why even the largest dinosaurs could only grow so big).
But because these stories incorporate certain tropes - e.g. spaceships, robots, laser guns - they are still considered science fiction, as opposed to fantasy, which features different tropes like spells or dragons. Some examples might be Dr Who, Star Wars, Red Dwarf, Farscape, Space Battleship Yamoto, Warhammer 40k, the Guardians of the Galaxy movie (not the original Marvel superhero comic which belongs one level lower). In Japanese anime or manga this includes the "super robot" category which features giant sized, completely implausible mecha, including Mazinger Z and Transformers, Guilemmo del Toro's Pacific Rim being a Western adaptation. Giant monster stories like King Kong and Godzilla would naturally also be included here.
3. Space Opera. The term "Space Opera" was originally used as a derogatory term for cheesy science fiction. It tends to feature melodramatic adventure, space battles, futuristic weaponry, larger than life heroes, a galactic scale, and scant regard for science, which is there only for storytelling purposes rather than realism or central to the story (technically Star Wars is also space opera as it features all these things, although its opening lines - a long time ago in a galaxy far far away - define it as science fantasy or science fairy tale).
Examples in this category include E. E. “Doc” Smith's Lensman series of the 1930s and 40s (the original "Space Opera" science fiction books which largely defined the genre, along with the Buck Rogers and Flash Gordon matinees), the German Perry Rhodan series currently numbering hundreds of novels, the epic French graphic novel series Valérian and Laureline (or Valérian: Spatio-Temporal Agent) by Pierre Christin and Jean-Claude Mézières, a number of SciFi television series like Star Trek, Battlestar Galactica, Babylon 5, and Stargate, which tend to feature more logical or more technical writing than the previous level. Although there are still many absurdities, for example, the All Members of Aliens Race X are Warriors (Klingons)/Logicians (Vulcans)/Philosophies (Minbari)/etc. Marc Miller's Traveller roleplaying universe served as a science fiction equivalent of Dungeons and Dragons, based on literary SF Space Opera. For movies the Aliens Franchise and the Wachowskii's Jupiter Ascending, (while not space opera) Terminator franchise, and Zombie apocalypse if explained by a virus (rather than supernatural). Various online space adventure, exploration, trade and/or combat games, like Eve Online, Elite: Dangerous, Star Citizen, and No Man's Sky are based on the standard scifi universe established by Star Trek, Star Wars, Babylon 5, and so on. In anime and manga, the "real robot" category, in which mecha are explainable by real world physics, like Super Dimension Fortress Macross and Mobile Suit Gundam, and the Battletech / Mechwarrior universe of piloted robot war-machines might also be included here.
4. Non-Hard Science Fiction. Here we transition from movie, TV, and video-game "scifi" to literary science fiction as such. There's so much science fiction that could be listed here one wouldn't know where to start, and in any case it wouldn't be much use simply listing science fiction stories and genres that, while not attempting to follow hard science, are not about scifi space opera either.
There is, however, also those TV/movie scifi space operas with more thought put into the story and worldbuilding (the creation of a fictional universe) and so could probably go one realism level up. Here, science and super-technology is fantastical but is better explained within the context of the story or universe, and there is less over-the-top tech like force shields, matter teleport, time travel, which are all staples of the previous two categories. Joss Whedon's Firefly/Serenity is set in a single solar system with a large number of planets, although the Wild West elements add absurdity, Cowboy Bebop is interplanetary rather than interstellar and features O'Neill Space Habitats, the StarCraft strategy game features non-humanoid alien races with their own cultures and background, and Mass Effect is one of the few video games that, in the original series, featured an intelligent story.
A frequent theme in all space opera scifi (due to it being filmed in a studio) is gravity being perpendicular to the direction of travel, just like being in a ship or aircraft on Earth. In an actual present or actual future spacecraft following Newtonian physics, gravity is caused by acceleration. In terms of literary science fiction, there's now even self-published science fiction which, inspired by TV/movie scifi rather than (as was the case in the past) by literary SF, also has this; these instances are usually explained by gravity plates, artificial gravity generators and the like, none of which have the slightest scientific plausibility.
5. Medium Science Fiction. This category includes science fiction that is stricter than Soft science fiction, but still not intended to be "Hard" or rigorous in the physics department, although it may still feature scientific concepts. Examples here include the 1950s movie Forbidden Planet, Frank Herbert's Dune (with its rich cultural and ecological references,) Heinlein's Starship Troopers, which established Military SF as an authentic subgenre, Alfred Bester's The Stars My Destination, Niven's Known Universe setting, David Brin's Uplift series, and Iain M Banks Cultureverse. The Dune and Cultureverse are especially considered to be classic works of Space Opera, as the term has been redefined to include more serious science fiction.
Here the humorous neologism "unobtanium" is relevant. This refers to materials that have not yet been discovered but which are necessary for the story. Both Niven's Ringworld, part of the Known Space series, and Banks Orbitals cannot be built with any known material and hence require "unobtanium". The related term "handwavium" is sometimes used to refer to some hypothetical future discoveries which cannot be extrapolated from current science and technology, such as artificial gravity reactionless drive.
6. Firm Science Fiction. As with Medium, this level is transitional between "soft" and "hard" science fiction. Here the science is even more reasonably explained in the context of the setting, and there is less handwavium and unobtanium. Heinlein's Citizen of the Galaxy, Arkady and Boris Strugatsky's Roadside Picnic, Orson Scott Card's Ender's series, CJ Cherryh's Alliance-Union universe, anything by Peter F Hamilton, Neal Asher's Polity universe, James S.A. Corey's The Expanse series and resulting TV series, and epic Space Opera like Alastair Reynolds Revelation Space/Galactic North Universe and Ann Leckie's Imperial Radch trilogy (Ancillary Justice and sequels, very much a successor to the Banks Culture universe) are some good examples. Hannu Rajaniemi's The Quantum Thief and sequels present a very different type of science fiction with strong transhumanist elements (Transhumanism being the philosophy that says that humans can and should transcend their present condition).
7. Medium-Hard Science Fiction. This tends to limit handwavium to a single dramatic device, such as FTL or stardrive, the rest being explained in a logical manner. Stories are often physics heavy. Some examples might include: Asimov's Foundation Series, Heinlein's Farnham's Freehold, Haldeman Forever War, Larry Niven and Jerry Pournelle's The Mote in God's Eye, Greg Bear's Forge of God books, Bruce Stirling's 1985 novel Schizmatrix (Shaper/Mechanist universe), Stephen Baxter's Xeelee Sequence, Vernor Vinge's Zones of Thought series, Alan Dean Foster's Humanx Commonwealth series, the Ad Astra board games, and Christopher Nolan's 2014 movie Interstellar (allowing for the limitations of cinematic plot devices)
8. Hard Science Fiction. This extrapolates from the known laws of physics, with only minimum handwavium for story purposes, and as much adherence as possible to thermodynamics and real science. Interstellar travel is either relativistic or involves a plausible device like wormholes that doesn't contradict Einsteinian physics. Tech is consistent and well explained. Arthur C. Clarke's 2001 series and Rama novels, Asimov's The Gods Themselves, Hal Clement's Mesklin series, Fred Hoyle's The Black Cloud, Gregory Benford's Galactic Center Saga, Carl Sagan 1985 novel Contact and resulting 1997 movie, Stephen Baxter's Manifold Trilogy, James Cameron's 2009 movie Avatar (which attempts a realistic biology and eschews FTL), and Greg Egan (whose work features rigorous mathematics, or humans living as computer simulations). David Pulver et al's GURPS Transhuman Space roleplaying system, Charles Stross's Saturn's Children and Neptune's Brood, and Peter Watts' Rifters trilogy and Firefall series, all feature various transhumanist themes like nanotech, realistic spaceships, solar system colonisation, and posthuman species. Some of these books could perhaps equally be placed in the Ultra Hard category.
But while Transhumanist concepts such as nanotech and mind uploading are considered hard SF, they may not always remain so. It's worth remembering that any gradation of realism in science fiction is very much based on the understanding of the time. Classic science fiction stories such as Jules Verne's Journey to the Center of the Earth and From the Earth to the Moon, and HG Wells War of the Worlds, while now absurd, were when written authentic hard SF when using the knowledge of the day, with Jules Verne stories being further on the Hard SF spectrum.
Margaret Atwood's post-apocalyptic Oryx and Crake and sequels may also be given a Hard SF rating. In parallel to this gradation, Atwood distinguishes between "speculative fiction" like her own work and "science fiction" which she associates with absurdist "talking squids in outer space" or things "we can't yet do or begin to do." Clearly, what she calls "speculative fiction" is simply a synonym for "hard SF".
9. Ultra Hard Science Fiction. This only builds upon known laws of physics, and does away with handwavium and unobtanium altogether. Interplanetary vessels have limited thrust, and because of lack of FTL the setting is often interplanetary only. Some examples are Heinlein's The Moon Is a Harsh Mistress, the first two books in Robert L. Forward's Rocheworld series, anything by Kim Stanley Robinson, Stephen Baxter's NASA Trilogy, Paul McAuley's The Quiet War series, Andy Weir's 2011 novel The Martian and the 2015 movie of the same name, Alfonso Cuarón's 2013 movie Gravity. For an excellent coverage on anything to do with space-based Ultra Hard Science Fiction, including real rocket science, see Winchell Chung's Atomic Rockets website.
10. The real world. Also known as nonfiction.