If memory serves.....
Carbine is actually from the French design Carabine, which I believe is "rifle".
Louis-Étienne de Thouvenin developed one of the first, if not THE first, version of the carabine, which was the design that inspired the Minnie Ball.
Why is that relevant? Because the Minnie Ball was the precursor to modern rifling.
So the term "carbine" is referring to a short barreled "rifle" - a weapon that shoots ammo that spins on it's axis.
And if that's not right someone will be along to correct me, but in the meantime you have a great piece of history.