Here's a breakdown right out of the PDZ manual of all the multiplayer gametypes:
DeathMatch is a creation of dataDyne Corp. Players compete in virtual arenas using any of several different groups of weapons. The mainstream game has swept around the globe, and the top-ranking DeathMatch players are feted as celebrities. Away from the rigid structure of the ranked matches, anything goes; some players even spice up the gameplay with bots...
A free-for-all match. The winner is the player who racks up the most kills.
A team only match. The winning team is the one that achieves the most collective kills.
Capture The Flag
A team only match. Each team tries to grab the flag from the enemy base and return with it to their own base, thereby capturing it. The team with the most successful captures is declared the winner.
A team only match. Teams try to capture several neutral hills and retain control of them until they generate points. The team that seizes and holds the most territories is the winner.
Dark Ops DarkOps is a round-based multiplayer game. It is a slower-paced and more tactical game than DeathMatch. Each round, players must buy weapons from their personal stock of cash, earned through killing the enemy and achieving scenario objectives.
A team only game. The last team with any members left alive wins.
A team only game. One team defends a base, gets one life each and can buy weapons as normal. All other teams have only basic weapons but infinite lives. The team that stays alive longest while defending the base wins.
A free-for-all game. There are two factions of players: infected and uninfected. Most players start off uninfected. After a player dies, he/she becomes a member of the infected. If the uninfected stay alive until the end of the match, they are the only players to get points. If the infected wipe them out, they are the only ones to score. The player with the most points is the overall winner.
A team only game. Targeted destruction-the team that ultimately causes the most damage to the other team's property wins.