To add briefly too what the guys have said-
Boxer priming system invented in Europe, but used in the US. Each primer has it's own anvil (priming compound is in between primer cup and anvil)
Berdan- invented in US, used in Europe- the cartridge case has the anvil, and a flash hole on each side of the anvil. Look into a Berdan case, 2 flash holes. Look into Boxer, one flash hole.
Berdan's CAN be reloaded, but are a PITA to do, need different loading tools. Either one CAN be corrosive. There have been other priming systems, such as Martin or Benet, but they are obsolete, you will not see them except on an antique cartridge.