If you check Webster and such you will find that it was a shortened rifle that could be used on a horse, a Calvary tool. All modern versions are just short barreled rifles, although the company may or may not make a longer one. For example, I had a Remington Model 74 Carbine in 30-06, it was a great little gun. The barrel was 18 inches, short for a 30-06, but much more handy than the normal 22 inch barrel. I also have a Ruger RSI,Carbine, in 308, once again, an 18 inch barrel.
Then of course the British 303 Jungle Carbine was a shorter version of th service rifle and the M1 Carbine was just a cute little guy. And Ruger has their Deerstalker carbine. One their website Rossi calls all of their lever action guns rifles, from the 16 .5 inch barrel to the 24 inch barrel.
But then the Remington Model 7, with it;s 20 inch barrel was always called a rifle. But then the Rem Model 600 with it's 18.5 inch barrel was a carbine, and so was the cheaper version, the later model 660 and or Mohawk which had a 20 inch barrel.
So, they just call short rifles whatever they want to call them. Personally, all of my AR type guns are the carbine length, just because if I want a long gun, I take a real gun with much more power.
But then there are the pistol caliber carbines.... nobody is going to call his long 9mm semi auto a rifle....just saying, it does not matter..