Looks like you have a really nice old 1896 Krag Carbine. From the pictures yours does not appear to be a cut-down rifle. They are really slick old guns. Common piece of advice is to have it checked by a really good gunsmith before you attempt to fire it. Seems that those old receivers were 'single heat treated', (as were the pre mid-1917 Springfield 1903s) and many have come un-glued during firing. Have the action and the bolt lugs/recesses checked for stress cracks.
I have an 1896 rifle and still shoot it every couple of years. I load mine with 150 or 173 grain .308 diameter FMJ bullets with a mid-range charge of IMR 4895. Very pleasant and accurate to shoot. The action is butter smooth.
Cavalry and artillery troops generally used the shorter Carbines because the longer Infantry rifle was not practical for their use. The Infantry liked the longer rifle because of greater long range accuracy and the longer barrel made a bayonet more practical. Thats about the best definition I can come up with for you. Enjoy!
Looks like it could be a (very nice) original carbine length gun; you may want to do some research on this one and verify it's history a bit more. The Krag is a very smooth action and is wonderful to shoot. They were sold by the DCM (CMP now) and many rifles were altered to carbine length either by armories or individuals; quite a few were sportered by the owners; as a result there are less original carbines and untouched rifles than ever.
An original carbine would command a premium from a collector point of view; do a little digging.
It looks like a real carbine, but better pictures would be needed to be sure. All Krag carbines had 22" barrels, so any other length was an alteration.
There were serial number ranges where more carbines appear, but there is no way to tell from the number if the gun was made as a carbine. The receivers were made and finished, then put on the shelf until needed for assembly. If the next orders were for carbines, carbines were made; if for rifles, rifles were made, without regard for which receivers were picked.