Appalachian crossbows with the cover over the arrow/bolt groove are technically slurbows, a subset of crossbows. There is a theory out there that they are descended from African models, but there is really nothing about their construction that links them to that area. Notably, the trigger system, the big mechanical feature of a crossbow, is quite different - African crossbows (which are themselves a copy of low-end European models) use a lever along the bottom that bumps up a peg which forces the string out of a notch in the stock. Appalachian bows use a trigger system like a gun, but are usually pushed forward, not pulled back.
OTOH, during the 18th and early 19th century there was a bit of a minor fad for slurbows among the British landed gentry, which were built very much along the lines of fine contemporary sporting guns, just with short slotted iron or brass barrels and a prod (the technical term for the bow) for propulsion. There are some nice pictures out there on the net, and I think Ralph Payne-Gallwey illustrates a couple in his book on crossbows (written at the end of the 19th century).
The Appalachian crossbows look to me like a redneck reverse-engineered version of the aristocratic slurbow - all wood construction, but built along the lines of a firearm, not a medieval or African crossbow. I imagine they originated when some poor but bright guy saw and maybe shot a European slurbow, imitated it in wood, but didn't know how the trigger system worked and came up with his own system. I'd love to make one, but haven't been able to figure out how the trigger works!
