Common Shotgun Action Types
Single Shot Break Open
The Single shot break open is generally the least expensive type of shotgun available today although there are some relatively high dollar trap shotguns such as the Browning BT99 that use this type of action. The action of most break open shotguns are opened by pressing a button or lever on the top of the receiver. Russian Baikal shotguns will have a lever in front of the trigger guard.
Bolt action
Bolt action shotguns are comparatively slow to operate. They may be single shot or will have a magazine holding one or two rounds.
Inexpensive to manufacture these used to be quite common but they do not enjoy the popularity that they once had. Marlin is the only manufacturer that I am aware of that still makes a bolt action shotgun. There are still quite a few of these old guns around and I still see them occasionally in pawn shops and gun stores. For the most part, bolt action shotguns are very sturdy but most of the examples that I have seen are well used or abused.
Lever Action
The lever under the receiver is moved forward causing the bolt to move backward, extracting the fired shell from the chamber. At the limit of travel the hull is ejected from the gun. The lever is then brought back causing the bolt to move forward striping a shell from the magazine and pushing it into the chamber. Most original guns of this type are collectors' items, particularly Winchesters made before 1900.
Double Barrel Side by Side
Break open shotguns are usually opened by moving a lever on the top of the receiver to the right. May have one or two triggers. Older designs may have hammers that need to be cocked, Otherwise will cock on closing the action.
Double Barrel Over & Under
Break open - gun is usually opened by moving a lever on the top of the receiver to the right. May have one or two triggers. Will cock on closing.
Pump
Reliable multishot, inexpensive to manufacture. Tubular magazine under the barrel. Generally there is a button in front of trigger guard to open action. This is the most common type in the United States.
Semiauto
Gas operated or recoil operated. Gas operated guns funnel a small portion of the powder gases to a cylinder which pushes against the return spring, opens the bolt, ejecting the cartridge case. The spring pushes a cartridge if there is one into the chamber and seats the bolt.