A better question is what are the different disciplines, as each has its own classes and requirements.
Fclass go to longrange target shooting.com and they have the official NRA rules basically, "open and FTR". FTR is limited to 308 and 223, while open is everything else up to 22 lbs and no muzzlebrakes basically.
BR- 600 and 1000 Both PA, IBS and NBRSA have rules, go to BR central and click on links there. Generally light and heavy gun with LG 17 lbs and under and heavy anything else up to 40 caliber.
Ground hog matches- no national rules, all local and differ from club to club
Egg shoots-- google Hickory Egg shoot as the most famous but not the only one.
Sniper/tactical no national rules, all local matches go to www.snipershide.com
in the forums and they have a thread on all of them.