if it's same sized then a SMG, then for the purpose of my comment its an SMG.
A carbine is a shortened assault rifle that fires assault rifle ammunition. SMG's fire pistol ammunition at a high rate of speed.
That's not always the case, however. Some carbines fire pistol ammo. Traditionally, it can be either -- when in doubt, if it's shorter or lighter than a "real" rifle, history has called it a carbine. This applies to Winchester and Marlin lever-actions (with the classic "cowboy" image of having a belt full of .44-40s that he could load into his trusty wheelgun
or carbine), into WWII with the De Lisle, and into modern day with stuff like the Marlin, Ruger, and Kel-Tec carbines that even take pistol
magazines, not just pistol ammo.
Sometimes a carbine is a short-barreled AR, yes, but sometimes it's a long barreled, stock-mounted, "pistol." Hell, technically an SMG firing on semi-auto fits the definition of a carbine...and even not-semi-auto ones (look up the official designation of the Sten gun some time). In real life, designations get all tangled up, definitions are loose at best, and terms are sometimes misrepresented.
What actually matters in this discussion, though, isn't really real life. It's the game, and the way the game is an abstraction of real life. Just like ammo is silly, just like weapon ranges are silly, just like armor is silly, firearm designations can be silly. Sometimes that means something we think should be lumped into Assault Rifles gets lumped into Submachineguns instead. If you want to house rule it, there's certainly nothing stopping you, but the long and short of it is that your average game designer just doesn't have the time or inclination to
really care about real-world guns, much less the time or inclination to try and make their future-fantasy RPG as realistic a combat simulation as possible.