Not every shotgun or rifle uses a pump, right? Right. So what's that thingy (for lack of a better term for now) worked back and forth that's sort of like a pump when characters use fully automatic and semi-automatic rifles and shotguns?
That thingy is called a charging handle or cocking handle. They're worked manually to load the first round into the chamber when ammunition is initially inserted into the firearm. After the first shot, the firearm automatically reloads a fresh round. They're present on the following firearms (yes, some of these terms mean the same thing).
Fully automatic rifles
Fully automatic shotguns
There's no need to work the charging handle again if the character pauses during a shootout before the ammunition runs out.
Make sense? This is only a quick overview without getting into the nitty gritty. Leave any questions in the comments.