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Design of the firearm
You do not list anything following.
You don't have anything following, but an example would be the typical double barreled shotgun.
You did not list any "following". Hardly fair to make us guess what they were. By the way, the image shown above is an example of a pump action firearm. The forend is "pumped" back and forward to eject a fired shell, and load a new one.
Two basic styles of firearm actions are single action and double action.
Half barrel is not a type of firearm action.
Type of firearm action
It is the action performed by the object.
No such thing. The Glock is not a double action firearm.
Action or reciever
Stock , Barrel & Action
The Gun Control Act 18 U.S.C. 921 (a)(3) The term "firearm" means (A) any weapon (including a starter gun) which will or is designed to or may readily be converted to expel a projectile by the action of an explosive; (B) the frame or receiver of any such weapon; (C) any firearm muffler or firearm silencer; or (D) any destructive device. Such term does not include an antique firearm. The Gun Control Act also defines "handgun", "rifle" and a series of other similar devices.