The damage dealt by a successful shot is determined by two things; the caliber of the round fired, and the location on the body that was hit. Damage is consistent across calibers, meaning that the 5.56x45mm round fired by an M4 does exactly as much damage as the same round fired by the M249. The 7.62x51mm round fired by the M14EBR-RI does more damage, and the 9x19mm round fired by the M9 does less.
There are two types of damage one can receive; instant damage and bleeding. Instant damage is as it sounds – an amount of damage instantly dealt to the enemy’s health. Bleeding is essentially damage sustained over time, and can be stopped by bandaging. Bandaging uses the [G] key by default, which must be held for ~2 seconds while still. Players do not bleed out to incapacitation.
An enemy will be neutralized with a shot to the head made with any weapon with the exception of the Remington 870 MCS shotgun. The head takes increased damage from each pellet to compensate, but a single shotgun pellet will not neutralize an enemy at full health. Shots to the torso result in more damage than bleeding. The pelvis is essentially evenly split, and shots to the arms and legs result in more bleeding than damage.