My personal definitions: A carbine is essentially a short rifle. I define a carbine as a shoulder weapon with a short barrel that fires a handgun round or a reduced-power rifle round. If it fires a full-power rifle round, then it is a rifle or a short rifle and not a carbine.
A Model 1892 Winchester firing the .45 Colt round is a carbine. A Model 1895 Winchester is a rifle unless it has a barrel that is 24 inches or shorter, then it's a short rifle. An 1873 Winchester in .44 WCF (.44-40) is either a rifle or a short rifle, because the .44 WCF was developed specifically for that rifle and therefore is not a handgun round (despite its use in some SA and DA revolvers).
An AR-15/M-16 is a carbine. An AK-47 is a carbine. They both fire reduced-power rifle rounds.
Any rim fire shoulder weapon with a barrel equal to or greater than 22 inches is a rifle; under that, it's a carbine.
These are just my arrogant, personal opinions. YMMV.