Progressive
A three stage reloading press is also called a progressive press. Contrast it with either a single stage press or a turret press, which tends to be used for one-at-a-time precision reloading. A single stage press handles one of three reloading stages, then another, then another--processing a batch of ammo one stage at a time: powder, projectile, then primer.
Standard Progressive
Progressive presses handle the three stages consecutively, so at the end of one progressive process you have complete ammo, not another stage to accomplish. You can think of a typical progressive press as being a mini assembly line for reloading that adds efficiency to the process. They may have a hopper with casings that are fed into the process. Though it isn't necessarily the choice of precision shooters, because of its assembly line progression, it is often the choice of high-volume shooters, from those shooting a semi-automatic weapon such as an AR-15 or those who compete.
Case Feed
A case feeder is sometimes integrated into a three stage or progressive press. You can think of a case as being similar to a carton of eggs. Instead of one cartridge at a time being fed into the progression, a case of many cartridges are fed, then batch-processed. The press doesn't complete each stage on each cartridge simultaneously, but it does make each stage more efficient because a whole case of cartridges can be processed much faster in a single stage than a one-cartridge-at-a-time stage.
Shot Loader
Shot loading progressive presses are conceptually the same as brass cartridge presses, but are designed specifically for shotgun shells. While shotgun shells have a brass base, the shaft of the shell is vinyl and the tip is crimped closed. So, in the shot reloader, the progressive systems reassembles shotgun shells, installing a new vinyl casing and filling it with shot, rather than a single projectile, before crimping the end.