Well, traditionally there are four major categories of poker games: 1) Draw Games (e.g., 5- and 7-card draw); 2) Stud Games (e.g., Stud); 3) Community Board Games (e.g., Hold'em, Omaha); and 4) Novelty (Baseball, Indian, Pineapple, etc.)
Then there are two basic formats of the Game: 1) Cash/Ring; and 2) Tournaments (MTT, ST, SnG)
And three hand ranking-types of games: 1) High-Only (e.g,. hold'em); 2) High + Low (e.g., PLO8); and 3) Low Only (e.g., Razz)
And three betting structures: 1) Limit; 2) Pot Limit; and 3) No Limit
And three standard table sizes: 1) Full Ring (9 or 10 handed); 2) Six-Max; and 3) Head-Up
The three basic places/locations: 1) Casino; 2) Online; 3) Home Games
And so on...
As you can see, there are literally hundreds of combinations and variants of the game possible. Almost without exception, however, they all have one common goal: make the "best" five card hand. For most of these variants, the "best" means traditional hand rankings (e.g., a flush beats a straight). For others, "best" means the lowest possible hand ranking.
I personally suggest sticking with hold'em until you're a fairly competent player. Then add in another variant, like Omaha or Stud. Learning other games too soon can confuse more than help, but once you're very comfortable with Hold'em, the other variants will actually help you overall. Poker is, ultimately, poker, regardless of the type or variant.