Cyberpunk style guide, for the /srg/
Disclaimer: I'm just interested in cyberpunk, not a genre analyst with a degree. The sub-divisions here are the ones which stand the most distinct in my own opinion, not any divinely decreed ur-genres. They're here not to dictate what kind of cyberpunk is the True, Right One, but to give newbies and writers'-blocked older GMs something to work with.
What is generally (very generally) accepted to constitute "cyberpunk" is "high tech and low life", and most subgenres and styles are a result of people interpreting these things differently. At the very least, high technology being used to create or perpetuate a dystopian or at the very least unpleasant society is a cornerstone of the genre, but what constitutes "high tech" and more importantly "low life" is a matter of taste and opinion.
Subgenre 1: Bog-Standard Gibson
Examples: The Sprawl Trilogy, most Gibson books from before the mid-90's, (the original) Ghost in the Shell, the pop-cultural image of "cyberpunk"
This is the big one. It's perhaps the genre of cyberpunk with the most baked-in conventions - the story takes place in some urban sprawl ruled by incredibly powerful media, cybernetics and nanotechnology megacorporations, who almost all have some kind of dirty plan up their sleeves, and the Matrix is something you connect to by wires which creates a virtual environment in your head. There's a tendency for main characters to be "the oppressed but skilled everyman" - the main characters are gifted or talented people who've been embroiled in the machinations of the megacorporations and have to fight to get out, and they're usually flawed people who're nevertheless ultimately not bad on the inside. Megacorporations are incredibly powerful and usually not directly interacted with, the police are corrupt and huge criminal syndicates rule the streets. Everything is touched in some way by the fear of Japan coming to rule the world - people eat ramen like it was a hamburger even smack in the middle of Berlin, and corporate officials say "kanpai" when they toast.
The megacorporation in these works is generally immovable. It's not expected of the characters to change anything big - what's the most attainable is simply getting out from under the corporate claws. Characters have personal goals that usually boil together into a greater whole, for example targeting the same megacorporation, and grandiose, idealistic goals are both rare and usually ill-fated. It's usually the story of a group of quirky individuals forced together through circumstance in order to escape the grip of the corporations who have the rest of the world controlled through viral marketing and sometimes outright propaganda. "Evil" megacorporations are rare, instead tending towards the callous - while few of them will ever intentionally try to cause harm for no gain, even fewer of them will avoid causing harm if it costs just the tiniest bit of money or time.
Environments are usually concrete and glass, marking a huge building boom a few years or decades back - prestige buildings and corporate offices are stately and austere, while lower-class citizens and outcasts (which are mainly outcasts by choice, not by force) live in crumbling, neon-hung concrete husks. Vice and entertainment are common, and most of the time the society outside the characters' field of view will be busy drowning themselves in bread and circuses, rarely being malicious as much as simply uninterested.
The Pulp Show
Examples: Cyber City Oedo, Armitage III, Shadowrun Role&Roll
In essence, this is an affectionate exaggeration of the above subgenre - the megacorporations are sneeringly evil, the heroes are devil-may-care mercs and the society is twisted to the point of depravity. Megacorporations don't usually dabble in media or "soft" fields, instead vaulting into creating drones, robot soldiers or artificial humans - what's definite is that what they create will result in poor people being oppressed, robots/androids/replicants being massacred or something else incredibly unpleasant happening solely for the sake of financial gain for the megacorporation. The world has usually been ravaged by some sort of calamity, giving context to the ridiculous evil of the megacorporations - maybe Earth's environment was ruined and humanity took to Mars, or the city is the last bastion of humanity after a nuclear war. The sociopolitical commentary is usually harsh to the point of parody - important people, especially antagonists but also protagonists, are incredibly motivated and extreme about their beliefs, and the "masses" just slurp up whatever the important person of the day says. The police are laughably corrupt or even villainous, and public security is low to the point of being Mad Max - the police only show up on time when they have something to gain, and most of the time they just take care of packing down the evidence and blaming the crime on the scapegoat of the week.
While the megacorporations usually are immovable in the long run too, this subgenre usually progresses along a steadily increasing string of incidents perpetrated by a central mastermind, who then in the final episode gets brought low, though the general structure of the world still remains - the main characters won't remove the very idea of megacorps, but they will probably sink one or two almost for good. The characters' motivations are often shallow, sometimes even quintessentially punk - "because nobody gets to tell me what to do", "they killed my father" and "no future" are all equally valid motivations.
This is what Shadowrun players tend to call "pink mohawk", though not the most extreme example of it - there are mohawks, there are eye visors, there's Hollywood hacking and there are truck chases with one guy firing a minigun out the window as the Men in Black's cyberzombie catches up to the truck while bullets bounce off it. While the narrative isn't straight-out prioritized towards comedy, it's nevertheless a more light-hearted genre where there's almost always room for a joke, there are few bad endings and there's always something left to be happy about in the end.
Vaporwave
Examples: VA-11 Hall-A, all those looped GIFs you see in the cyberpunk threads, to a degree Snow Crash and other Neal Stephenson works
Basically, cyberpunk seen through the lens of a 90's kid who was born in 1996. A fusion of classic cyberpunk with 90's anime aesthetics and the "radical" millennial spirit of the late 90's, vaporwave focuses less on the oppressive technological corporate dystopia and more on a "post-ironic" sense of ennui, imitation and insincerity. Characters are, as a common trait, eccentric to the point that they'd be called strange, often obsessed with the past or the future - gimmicks are extremely common, whether it be an obsession with some kind of (probably Japanese) media or an innovative piece of cybernetics. The world is garish, logo-strewn and pastel-colored, with pink neon and blue hair - oversized sunglasses, Gameboy Colors strung on belts, decks that look like a Visual Boy, Vocaloid T-shirts and ironic katanas are the order of the day. There's a sense of stagnancy and postmodern boredom in the world, which at times overlaps with post-cyberpunk - a major focus lies on everyday life and habits, especially how habitual and unfulfilling it is in the long run, and many characters are freeters or layabouts to the classic cyberpunk genre's maligned but talented everyman. "Lazy but brilliant" defines the vaporwave protagonist - cutting-edge modern, street-smart, smart-ass, decked out in the newest cyber-fashion and yet still just a twenty-something drifting in an interpersonal void.
Megacorporations aren't particularly evil, but aren't good either - the order of the world is decided by individuals, and while this usually ends up in more of the same, the generic corporate board member usually has a face, a name, a personality, goals and a family. There's a pervasive focus on the past, but usually with a further focus on alienation - the new generations are growing up with new technology and losing connection to the past, which sometimes manifests in explosive though misguided activism. Everyone else accepts the future and rides on the wave, because everything else is just so hard to do.
Change is possible and even likely, but this is purely temporary - the ennui of living in an overly modern society, constantly inundated by logos and advertising, doesn't change just because someone took down a megacorporation. Vaporwave works often question, directly or indirectly, the value or worthwhileness of a victory, no matter how great.
Post-cyberpunk
Examples: Psycho-Pass, Serial Experiments Lain, William Gibson's Idoru
To put it simply, post-cyberpunk is cyberpunk viewed through the eyes of the people who define the society, even if the main characters are fighting against it. From the inside, even the most cackling megacorporation pays its wages, taxes and registration fees most of the time, and the employees eat lunch and talk in the breaks instead of going to a recharging station or just being worked all day long. People use nanobot surgery to change their hair color for a night on the town, gossip about that guy's daughter who just got cybernetics, jack into the Matrix every morning for an update on the news, discuss their opinions on artificial humans on their way home from work, eat krillburgers and soy shakes at the same old McDonalds, follow the development of simsense technology on  their pocket computer and talk about the days where people's body, personality, capabilities and potential couldn't be changed with enough money and time.
It's characterized by a sober, realistic approach to people's reactions to technology and innovation, and as such usually ends up being more investigation- and socially-focused than other cyberpunk genres - killing people isn't something you just do, and even megacorporations sometimes keep their heads down to avoid a scandal. Private armies and economical strong-arm tactics alone won't give a megacorporation world domination, if such a thing is even realistically possible - no, you pour money into the local government, industry and media, make your products well, advertise them well and hope to be liked. There's internal logic, no matter how twisted, in all corporations and organizations, and pure villains are as rare as are pure heroes. It's a rational, rationalized genre where narrative consensus doesn't avert a lot of consequences, and is usually populated by anti-heroes and villains with earnestly good intentions - of course, a lot of people "fall through the cracks" as well, and there's a lot of focus on who has to lose to make sure that 90% of society can have good lives. Post-cyberpunk societies tend towards actually being safe, comfortable and entertaining for everyone who's willing to suborn themselves, and the conflict comes not from straight-out villainy, but from happiness being limited to a certain amount of people who're willing to make certain sacrifices. As such, even the motivation behind more conventional cyberpunk protagonists is likely to be questioned, with actual weight behind it at that - in a pulpy cyberpunk work, there's no good reason why the iron-hearted, bright-eyed main character would ever accept a lifestyle that's probably literally built on mulched babies, but a post-cyberpunk work is much more likely to face the character with the fact that they're giving up on a perfectly safe and fulfilling life just to be contrary.
Games set in these kinds of settings are almost by necessity what the Shadowrun fandom calls "black trenchcoat", because post-cyberpunk works generally cleave towards the side of realism and suspension of disbelief when it comes to security and safety. People react realistically to intruders, security specialists are professionals and sometimes something just isn't possible - it's often markedly more "realistic" and at times unfair than other more narratively-defined subgenres of cyberpunk.
Dystopia All The Way
Examples: Texhnolyze, Ergo Proxy, Blame!
Works like this, most importantly, are usually defined by a central lose-lose situation which the characters are trying to extricate themselves from. The society of the setting is often straight-out irredeemable - if it's not straight-out post-apocalyptic, with cybered-up survivors and slavering mutants kept at bay only by sinister masked guards, it's a monstrous dystopia with people shot down on the streets by special forces for thinking unhappy thoughts into their constantly active mental imaging transciever. What separates it from pulp cyberpunk and just plain pulp splatter is that the brutality, violence, lies and manipulation are often ingrained in the setting to the point where it's impossible to remove it, or it's an acceptable alternative to some kind of unspeakable threat. As such, characters are often hard-ass, brutal mercenaries or super-soldiers whose hard shells are stripped away bit by bit to reveal vulnerable and messed-up people, and the antagonist is often diffuse and unknown at the beginning of the story. The setting is often ruthless, with characters being killed without mercy or remorse when it would make sense, and the dystopian elements are often played up to the brim - lawless, crumbling shitholes where people would kill for a scrap of soyfood and isolated, insular "utopias" where everyone has to carry sheaves of papers and ID at any given time and can be shot right there if one is just an hour out of date are both common.
Character motivations, if they're not as diffuse as "find something out there that's better than this", are often disproportionate or just desperate - in a world with such ingrained corruption and such deplorable conditions, it might be better to blow up the last arcology on Earth and have people scramble out to make lives of their own than it would be to perpetuate a safe but cruel dystopia. Murder, rape, torture and other otherwise exclusively villainous methods can show up in characters here, who're often simply villains and monsters who turn to extreme methods out of desperation or ennui.
Settings like this tend to have more of a sense of a lost history behind them - while post-cyberpunk rarely leaves the confines of the 21st and 22nd centuries, this kind of post-apocalyptic or power-dystopian cyberpunk is often set hundreds or even thousands of years in the future, with societies held up by twisted, outdated versions of the rules of the past. There's a distinct crossover with survival horror here, especially as soon as you go outside of the cities, into the worse parts of town or just touch on some of the more dubious bits of the setting - characters are much more likely to find themselves in the sights of something much more powerful than them, and indeed this subgenre has a large proportion of works with magical or psionic antagonists, sometimes crossing over into the Lovecraftian.