Gamemodes are sets of rules that are applied to the map and the players. Some gamemodes, like Control, also add objects to the map that need to be captured, delivered or destroyed.
Classic gamemode, where the only goal is to kill the enemy team and get to the score limit.
Variation of Team Deathmatch, where everyone is alone instead of being in two teams. Your goal is to kill all opposition and get to the score limit.
This is played with two teams. There are multiple flags throughout the map and they are captured by standing near them for a short time period. The goal is to hold all of the flags at the same time, or to hold more than the enemy team when the time limit ends.
This gamemode is played in two teams. The other team's players are normal and respawn normally. The other teams players are stronger and deal more damage, but they can't respawn. The normal team's goal is to kill the whole enemy team, while as the stronger team must survive till the end.
In Ragicide, one player is chosen to be the Champion, who has ultimate stats. The other team which consists of all the other players try to kill the Champion, while as the Champion must survive and get as many kills as possible.
This is played with two teams. The other team defends the pit, while the other team tries to bring bombs into the pit. When the attacking team's players spawn, they get bombs, and they have to deliver them through the map into the pit.
Assault is played with two teams. The other team defends and the other attacks. There are multiple points automatically owned by the defending team which they have to defend. The attacking team can only capture the one that's closest to their spawn. When a point is captured, the defenders are forced to retreat, and the attackers try to capture the next point.
Classic mode where two teams both have a flag in their base. The teams try to capture each others flags. The team with more captures wins.
Otherwise exact to CTF, but with a little twist. In Capture the Weapon, instead of capturing the flag, the player try to capture the Annihilator weapon. The player who captured the weapon moves slower, but can use the weapon to kill enemies.
Exact to Team Deathmatch, but played with four smaller teams.
Exact to Bombpit, but all four teams try to deliver bombs into the same pit. No one defends the pit, but the team who first gets a certain amount of bombs into the pit wins.
Exact to Capture the Flag, but played with four teams.