Short answers, pulled from the story.
A repeating rifle fires multiple times between reloads by storing cartridges in a magazine and feeding them into the chamber with a reciprocating bolt, worked either by hand or automatically. Chambering each round also recocks the hammer or striker for the next shot.
The term repeating rifle usually refers to manually operated designs such as lever-action, pump-action, and bolt-action rifles, while self-loading rifles cycle automatically using the recoil, gas, or blowback of the previous shot. Self-loading firearms are technically a subcategory of repeating firearms, even though the two terms are used differently in practice.
The Henry rifle was used by infantry and the Spencer rifle was used by cavalry during the American Civil War and the American Indian Wars that followed.
The Windbüchse rifle was the first repeating air rifle to see military service.
The earliest repeating rifle on record is the Kalthoff repeater, dating to about 1630, followed by designs such as the Puckle gun in 1718 and the Girardoni air rifle in 1779.
Autoloading, or self-loading, repeating rifles use blowback, recoil operation, or gas operation to cycle the action. Gas operation, in which propellant gas drives a piston that unlocks and cycles the bolt, is used by almost all modern military rifles.