Are there seperate models for the weapon in front during FPS view and of you and the weapon the way others look at you?
Or is there a camera or something that's level with the character's head and the weapon shows up in FPS view because it's held in the right place?

Both of those options are used by different games.
The first option seems to be the "traditional" method, being used in Quake, Half-Life, etc... The second option is used in the Op:Flashpoint/Arma series of games.