The Peacemaker bears a striking resemblance to the real-life FN Herstal 'P90 TR' submachine gun PDW (Personal Defense Weapon).
The real-life P90 can be considered as a carbine due to the fact it can chamber rifle ammunition. This explains the military drops, the military ammunition it uses and why it is considered a carbine in the game.
It is more commonly known as a Personal Defense Weapon.
The name Peacemaker may be a reference to the law enforcement, named Peacekeepers, from the movie The Hunger Games: Catching Fire. using FN P90s (Which the Peacemaker is based upon) as their standard issue firearm.
The name may also be derived from the assignment in Battlefield 4 "Peace Maker", where upon completion the player is free to use the FN P90 in multiplayer. 
The gun does not allow the player to use Grip attachments because of the design. This also affects the Yuri.
The Peacemaker is one of three bullpup designed weapons.