If you've never seen how a particular game works and want to get a feel, search around and watch an episode or two of the game online. Rollplay on Youtube has a good channel that covers a lot of different types of games. You can also find games on Roll20's channel as well, and many more on Twitch and other channels.
As for game types, many of the ones listed here are very tailored games meant to play a very specific kind of game. I'll try to give you a summary of some of the popular ones.
Apocalypse World (AW) is a game, as you'd expect, about playing as a group of survivors in a post apocalyptic setting.
Night Witches is a varient of AW about a female bomber squadron in WWII.
Dogs in the Vineyard is a game about faithful 'God's Watchdogs' that go around Mormon-esque towns helping the community and enforcing the judgments of their religion.
Fate Accelerated or Fate Core is a mostly generic system meant to tell a lot of different kinds of stories. Fate Accelerated specifically is a very short and very flexible rulebook for whatever you could imagine.
D&D or Pathfinder are games about playing a group of adventurers in a tolkien-esque fantasy world, generally combat focused but you can play a lot of kinds of campaigns in D&D.
Dungeon World is a 'rules-lite' version of D&D based on the AW ruleset, which basically means it has a lot less rules and is more focused on the collective narrative.
Shadowrun is a game about telling cyberpunk heist stories in a fantasy/cyberpunk futuristic city run by megacorporations.
Blades in the Dark is a game about a scoundrel crew building their gang up from scratch in a city roughly based on the Thief or Dishonored games.
There's many more out there, it just depends on the kind of experience your group wants to have. Many of these rulesets are wildly different and the rules are tailored to create a specific kind of experience. Some of these rulesets are more generic and meant to be used to play a wide variety of games. Some are 'rules heavy/crunchy' which involve a lot more mechanics while some are 'rules light' and deliberately involve much less. D&D, Fate, Pathfinder are examples of more generic rulesets, whereas Blades in the Dark, Apocalypse World, Night Witches, or Dogs in the Vineyard are much more specific.
In "My life with Master" the party play the henchmen of an evil master. It explores ideas of culpability, fear, self-loathing, humanity and, possibly, redemption. It is the only role-playing game to give me heart ache. Literally, pathos I felt as a physical reaction.
"The Clay that Woke", another by Paul Czege, concerns a race of Minotaurs, more physically powerful but utterly subjugated by humans. It explores themes of racism, power, imperialism, and ethics. Not quite as good MLWM, but very much worth playing.
I added "The Beast" to go all in on a game totally unlike D&D. It is a single player game, using cards and a diary, with an erotic theme, and dark overtones. I haven't finished my play through, and I'm not sure I recommend it, quite, but it has got under my skin.
"Hillfolk" is Robin D Law's 'Drama system', essentially game mechanics built around generating interesting interpersonal conflict. The setting is Iron Age subsistence, but it includes several other settings, from horror to modern life.
Funny mix of games, as most of them are rather new in RPG terms, while Shadowrun has been around since the 80s (and has maintained a mostly coherent timeline since first release).
If you've never seen how a particular game works and want to get a feel, search around and watch an episode or two of the game online. Rollplay on Youtube has a good channel that covers a lot of different types of games. You can also find games on Roll20's channel as well, and many more on Twitch and other channels.
As for game types, many of the ones listed here are very tailored games meant to play a very specific kind of game. I'll try to give you a summary of some of the popular ones.
Apocalypse World (AW) is a game, as you'd expect, about playing as a group of survivors in a post apocalyptic setting.
Night Witches is a varient of AW about a female bomber squadron in WWII.
Dogs in the Vineyard is a game about faithful 'God's Watchdogs' that go around Mormon-esque towns helping the community and enforcing the judgments of their religion.
Fate Accelerated or Fate Core is a mostly generic system meant to tell a lot of different kinds of stories. Fate Accelerated specifically is a very short and very flexible rulebook for whatever you could imagine.
D&D or Pathfinder are games about playing a group of adventurers in a tolkien-esque fantasy world, generally combat focused but you can play a lot of kinds of campaigns in D&D.
Dungeon World is a 'rules-lite' version of D&D based on the AW ruleset, which basically means it has a lot less rules and is more focused on the collective narrative.
Shadowrun is a game about telling cyberpunk heist stories in a fantasy/cyberpunk futuristic city run by megacorporations.
Blades in the Dark is a game about a scoundrel crew building their gang up from scratch in a city roughly based on the Thief or Dishonored games.
There's many more out there, it just depends on the kind of experience your group wants to have. Many of these rulesets are wildly different and the rules are tailored to create a specific kind of experience. Some of these rulesets are more generic and meant to be used to play a wide variety of games. Some are 'rules heavy/crunchy' which involve a lot more mechanics while some are 'rules light' and deliberately involve much less. D&D, Fate, Pathfinder are examples of more generic rulesets, whereas Blades in the Dark, Apocalypse World, Night Witches, or Dogs in the Vineyard are much more specific.