Pull your long BBL out of your carbine and lay it next to the short one. Compare the diameter of the BBL right where the chamber is. If they are the same diameter... you have an illegal short BBL rifle, so get it as far away from the carbine as possible and contemplate either (A) getting rid of it RIGHT NOW, or (B) sending it FAR FAR away for a vacation RIGHT NOW while you send in an ATF Form 1 to allow you to manufacture a short barrel rifle, or (C) keep and plan a nice vacation at Club Fed if you are ever caught with it.
There is a market for these BBL's, and the easy thing to do would be to give it to a friend who does not own a Uzi and then let them sell it. Registered short barrel rifles based on this platform are pretty common, as are people wanting them to make legal SBR's.
Now, here's what is most likely: You very well may have a submachine gun BBL, which is legal... sort of... with caveats.
"Most" of the short BBL's floating around are original SMG barrels and do not fit the semi-auto carbines without modification. The chances are that when you compare the two BL's you will find that the short BBL has a larger diameter at the chamber end, meaning that it will not fit into the carbine without being reduced in diameter on a lathe. If that's the case, you have the "makings" of a short barreled rifle, and if you send in an ATF Form 1 with $200 and wait about six months, you can then have the BBL turned down and have a legal short BBL rifle. Or you can just keep it as a curiousity.
If you do the latter, you still "may" be hassled... it's close enough to having an unregistered SBR that you "might" be construed to have constructive posession of same... make your life simple and either register the darned thing or get it outta the house.