I've seen very similar ones many times from civil war sites. But those are 20th-Century .22-caliber bullets (or perhaps .25-caliber), and thus your find is the result of target-shooting. They got fired into a target on a tree or a wooden board. One bullet hit right on top of the other in the wood. (Like Robin Hood splitting the arrow with his second shot.)
Ebay sellers claim these are the result of two bullets hitting each other in mid-air. But that is a false claim, because to "join with" each other in mid-air, they'd have to be fired from opposite directions, and thus would hit each other nosetip-to-nosetip. See the photo attached below. "Joined" fired bullets which aren't nose-to-nose were fired from the same direction, and hit the exact same spot on a tree or "hard dirt" hillside.
Edit: CriticalRecovery and I were typing at the same time.