Nope that is pretty much it. A carbine is a shorter version of a rifle.
Lots of history involved - heck many people consider the 20" rifle to be a 'carbine' in comparison with some of the older rifles.
Lowers at Bushmaster are all the same they can come with a variety of different stocks. Generally you'll only see the faux telestock on carbines - but there is no reason why you can't have a lower with this stock on a rifle (other than it would look silly).