DICE has documented the five Battlefield 3 multiplayer modes. They are Team Deathmatch, Squad Deathmatch, Rush, Squad Rush and Conquest.
Each of the five modes can be played on each of the nine Battlefield 3 maps available at launch.
Team Deathmatch supports two teams of 12 players (24 in total). The goal is to reach a kill-count before the other team. There are no vehicles in Team Deathmatch.
Squad Deathmatch is for four teams of four (16 in total). Again, the goal is to reach a kill-count before the other squads. An Infantry Fighting Vehicle can be used. An Engineer can repair it.
Rush is for 24 players on console and 32 players on PC. The goal is for the attackers to destroy all M-Com stations, and for the defenders to kill all the attackers. Defenders have unlimited tickets (respawns). Attackers gain tickets by destroying M-Coms.
Rush has lots of vehicles, including transport vehicles, armoured vehicles, helicopters and jets.
Rush was available in Bad Company 2 but has been tweaked for BF3. You cannot use explosives on or shoot at M-Com stations, you can only arm or disarm them. If all the attackers die after an M-Com is armed, the game continues until it blows up or the defenders disarm it. If a defender begins disarming just before the timer runs out, the explosion will be prevented until the disarm is finished. If a defender is shot and killed while disarming, the M-Com will instantly blow.
Squad Rush is for two teams of four (eight in total). It's the same as Rush but more intimate. There are only two bases with 1 M-Com station per base. There are no vehicles in Squad Rush.
Conquest is for 24 players on console and 32 on PC. This is the famous all-out Battlefield warfare mode. Big maps, all the vehicles. The idea is to capture and hold flags. Doing so drains the opposing team's tickets. The first team to run out of tickets loses.
Those are the base multiplayer modes. But you can tweak them. You can opt for Infantry Only and get rid of vehicles; you can select Hardcore Mode to remove the game's interface help.