Good question, I haven't played long enough to know all the game modes, I bought my copy a few weeks before gears so I stopped to play that of course. The booklet states:
Eradication - A team-only game. The last team with any members left alive wins.
Onslaught- 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.
Infection- 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 unifected 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.
Sabatobe(insert beastie boys song)^^ -A team-only game. Targeted destruction-the team that ultimately causes the most damage to the other team's property wins.
I think I've played all of the types just didn't know it and or the particulars.