For me, a cover is a rendition of a piece previously written and performed or popularized by someone else. Sales or airplay aren't particularly critical. What I always find interesting are tri-generational covers where the original is unknown to the listener, or cases where the original is generally obscure, often true of rock songs originally from the blues canon, e.g. "Crossroads".
I'm fairly well-versed, musically, and I take a small perverse pleasure in responding to "Have you heard X's new song?" with "Actually, that was originally recorded by Y z years ago."