In Paintball there is quite a few different games,  Here is the ones I managed to find.


Attack and Defend:
Defending-The defender has a certain area they are supposed to stay in, and they cannot leave the boundries, if a player does, they are out. The point when defending is to get as many attackers out as you can within the time limits, and have at least one person remaining when time runs out. One defender left at the end of the game means the defenders win.

Attacking: Your objection is to eliminate all the defenders within the time limit. If you succeed and eliminate all of the opposing team's (defender's) players you win.

Civil war:
Even teams, Lined up to even lines in an open field, both teams facing each other. Both teams must have velocitys set low, each player must have 3 paintballs with no hopper. Players load balls one at a time and shot as a team.
team with most players left after all rounds are shot win.

Terrorist: The terrorists job is to hold hostages and defend them from being released by SWAT, or "kill" them before SWAT can safely release them. The terrorists normally also have a bomb that they must guard untill it explodes, and not allow a member of the "bomb squad" reach and defuse.

SWAT: Your job is to get to release the hostages from the terrorists without the hostages being "killed." If you are a member of the bomb squad, your job is to reach the area where the bomb is, eliminate the terrorists guarding it, and defuse it.

Scenario: Scenario games are games that simulate real wars and missions, except you use paintball guns instead of real guns. Like you could play Desert Storm, and dress up in desert camouflage and camouflage face paint then wear helmets and vests with pockets for things like walkie talkies and such. 

Speedball: In Speedball you play with two teams and they each start at a different side of the court, the ref says go and you run for cover and try and shoot everyone on the other team, before they shoot you.

Woodsball: In woodsball you play in the forest with natural covers like trees and bushes, there is not really an objective except to eliminate the other team.

Airball:  Airball is a fast paced game that is played in flat arenas or stadiums with artificial blow up bunkers, each team starts on a different side of the arena and then when the go whistle blows you run to the bunkers and try and get the flag from either the center or other side of the arena.