Over the years I try to use terms in their correct definition, so I checked the definition of "carbine": a light automatic rifle
Historically, the term was applied to "a short rifle or musket used by cavalry."
So under the old meaning, even a muzzle loader would have been called a carbine.
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I love discussing military history. After looking at the current definitions of the word Carbine, I think the only thing we can agree on is the definition has evolved.
From my readings, the origin of the word was from the French and they armed their cavalry during the Napoleonic wars with short muskets that fired small or pistol caliber bullets (mind you, the Brown Bess was practically a .50 caliber rifle so YMMV).
So from what I could gather the traditional definition was a long arm using small caliber ammunition. The classic example would be the .30 M1 Carbine which was designed from the ground up to use a new .30 round. Hot by pistol standards but not compared to the .30-06 used in the Garand.
In the same war though the term was applied to shortened versions of a long-arm like the so-called Enfield Jungle Carbine (No 5 MkI), so that means it meant different things to different people.
Brittanica just defines it as a long arm that has been shortened from its original length (a definition that doesn't encompass the M1)
Wikipedia goes on to add a definition that make them either shortened versions of a long arm or rifles chambered for a less powerful cartridge (a definition that does and covers PCCs as well).
I guess its become a catch-all term for a long-arm (non SMG/PDW?) that's meant to fill a role subordinate to a Main Battle Rifle.