You are getting a bit confused with the BF series DC. There are loads of different games in the franchise and the Bad Company games are actually different games with their own story about the USA fighting Russia.

The original BF2 was the third game in the franchise and was only every released on the PC, in 2005, but the later version of the game called Battlefield 2: Modern Combat was released for consoles, on the 360, as well as the PS2 and original Xbox (but never released on the PS3) .

The main Battlefield games have single player campaigns, but the main focus is on the multiplayer gaming, where you enter a warzone "level" that is a free roaming world just like other multiplayer games like CounterStrike. Picking one of 2 sides, you can go anywhere, jump in a vehicle, tank or gun emplacement and use them, or get in a plane and fly around the level shooting and other players and dropping bombs. When you die you respawn, normally back on your aircraft carrier or one of your captured flag points. It is great fun.

Battlefield 3 is the first game in the main series to be released on the PS3.