PPC - Practical Pistol Competition
Mostly revolvers shot using the same type of "stages" for all matches.
GSSF - Glock Sport Shooting Foundation
Glocks shot using the same type of "stages" for all matches.
USPSA - United States Practical Shooting Association
Two "segments" of pistol types, Limited and Open. In Limited, you can only make limited types of modifications to the weapon. No electronic optics or compensators. Open guns, anything that is safe goes, comps, optics, slide rackers, thumb ledges, etc.
Stages will vary from match to match with a "classifier" stage that each club sets up identically. After shooting 3 classifiers, you are given a category (or classification) in which you compete against others with similar abilities.
All the shooting competitions have really friendly people. I suggest that you watch or go to a practice and ask questions. Everybody I know just loves to talk about their guns!!
"...What will you do without freedom? Will you fight?... Fight, and you may die, run and you'll live, at least a while. And dying, many years from now, would you be willing to trade all the days from this day to that, for just one chance, one chance, to tell our enemies, that they may take our lives, but they'll never take our FREEDOM!!!"