I do have a question that may benefit those of us who find we like the system: What are ALL of the DnD types used on Elliquiy and are there just minor differences or are the differences major to what we will be working with? If minor, could you explain the differences?
You sent us straight over the deep end, Dragongoddess....

OK, let me put it simply: ALL editions of ALL games are played by someone, somewhere. I remember on another forum a guy said he wrote some minimalist rules as a joke, never playtested them, and didn't expect anyone to play them - ever. They just sat on his website.
That is, until he received an e-mail from a Japanese guy who said their group had just concluded a year-long campaign using his system, and they wanted to continue. But before committing, the unnamed Japanese GM wanted to know, is the author working on the next edition

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If we were to focus just on D&D editions, here's a simple breakdown. Note I said "simple", not "short"

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You can skip it safely, though. No, really.
OD&D is the first D&D edition, and the first RPG published, in 1974 IIRC (I wasn't born yet, either way). It's actually quite elegant in its simplicity, as long as you're fine with more abstract things - for example, all weapons do the same damage (1d6). Reasoning: all weapons have a chance to kill you. The GM can give you a bonus for having the better weapon, of course...
It's still being played, and probably will be for as long as there are RPGs.
The next few editions (B/X, BECMI, Mentzer, AD&D, and so on up until AD&D2e) get less and less complex, on the price being: more rules. I lump them together, because people often mixed and matched them, in practice (or so I've been told - I've only seen the books for one of those). In reality, you can even mix them with OD&D - it's not like there's a definite line, and the "engine" is robust enough to take it.
All of the above have "clones" nowadays. Some clones are notable for adding and discarding some elements, achieving different effects. Some of my favourites make the game better suited to Swords and Sorcery games in the style of Conan, Fafhrd and the Grey Mouser, Red Sonja, and the like (DCC RPG, Crypts and Things, and arguably, Low Fantasy RPG). Others make it more suited for Dark Fantasy, in the style of Elric, Dragon Age, and their ilk (Crimson Blades, for example). A game like Backswords and Bucklers gives you the opportunity to pubcrawl London in the age of the Tudors. The Adventurer, Conqueror, King System (ACKS) gives you the opportunity to follow Conan's path, starting as an adventurer, and carving out your domain, then ruling it...hopefully wisely.
Others...well, just give you more material to play with, being in essence the author's houserules.
Collectively, the "not quite clones" are known as the OSR (Old School Renaissance). If you sense me being biased towards those, that's true! I just find them most fun. That's probably due to the GMing ethos, though, which says "if you can think of something, you can always try it" (though learning magic as a warrior is out, for most games).
Then we get to Third Edition (often abbreviated to "3.5").
It's a complete re-boot, you can't mix material published for it with material for the previous editions (well, you can - but it's like adapting material from a different game). It's also got orders of magnitude more rules. Some critics, me included, claim that it takes some very hard jumping through hoops to make sure the non-magical classes remain useful. Of course, that might be a feature for some.
The edition is most notable for giving much more options to mix and match when building your character - special abilities of different classes, special abilities "everyone can take", magic items, spells, spell-like effects, and so on. Those combine in interesting ways, and some people outright state that making an optimized character is a major part of the fun. Want a barbarian wizard who resorts to spells when his barbarian rage isn't enough? Sure, you can do that. (I think it's not really optimized, but it's a combo that's outright impossible in many previous editions).
You'll also hear about Pathfinder. Everything that's true for 3.5 is true for PF as well, since it's based on 3.5 to begin with, just like the OSR games are based on the earlier editions. I prefer other games based on 3.5, like Fantasy Craft.
There's Fourth Edition: Really codified, rather good for tactical combat with grid and miniatures. It's also the least popular on forums, because the grid and miniatures are hard for forum games - and because a fight usually lasts at least 45 minutes in real time. I guess that's too long for forum games?
That's the one I have the least experience with - though it makes martial classes mostly equal to magical ones.
If I wanted to play something like it, but lighter, though I'd rather use 13th Age (because it relies less on grids). 4e is also, basically, a separate game from all previous editions - convert at your own risk.
And the current Fifth edition (5e) is streamlined, and plays like a hybrid of 3.5 and 4e with some elements thrown in from earlier editions - but most of it is from the previous two.
Also a separate game.
You must understand this, though: all editions of D&D and all games that aren't D&D, have advantages and disadvantages. There's no perfect game. There's only "perfect, or close to it" for a specific game, with a specific group!
Some people like codified rules and knowing what the effect would be. Others prefer to improvise on the spot, and having the GM adjudicate. That, right there, is a major difference between, say, 3.5 and earlier games.
The important part is knowing what you like...
And then you're going to play what the GM is willing to run, anyway

. But you can at least try everything, and maybe look for a specific game next time.
Oh, and there are many, many other games out there. All possible genres are covered already, I believe. Some games are even multi-genre, like GURPS, BRP and arguably, Traveller.
A major difference between D&D and most other games is, however, that usually, editions of a game are "mostly compatible". Different editions of D&D are different games that play differently, especially the most recent ones.
Don't sweat it, trying to learn all of the above! If you find it fun, you'll learn in time. You can just Google a genre's name and "tabletop RPG" some time. You might be surprised what you could find under "wuxia tabletop rpg", for example

! Reviews are really helpful, and sometimes funny.