Provenience: The precise location where an artifact or archaeological sample was recovered archaeologically.
Provenance: The detailed history of where an artifact has been since its creation.
Take as an example a Roman coin. The provenance of that coin could include its creation in a mint in Italy, its loss in a shipwreck off Alexandria, its recovery by shell divers, its purchase first by an antiques dealer, then by a tourist who left it to her son who eventually sold it to a museum. The artifact's archaeological provenience would be the location in the shipwreck where it was found.
When archaeologists lament about the loss of provenience from a looted art object, what we really mean is that part of the provenance has been lost--we are interested in how the coin got from the Roman mint into the museum; while art historians don't really care, since they can generally figure out what mint a coin came from. "It's a Roman coin, what else do we need to know?" says an art historian; "The shipping trade in Roman era Mediterranean Sea" says an archaeologist. I should have known: it all comes down to a question of context. It's interesting, don't you think? Because provenance for an art historian is important to establish ownership, but provenance is interesting to an archaeologist to establish meaning.
As reader Eric P so elegantly put it, Provenience is an artifact's birthplace, while Provenance is an artifact's resume.
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