"Cover" was originally a term coined to describe white pop singers who would be given songs recorded by black artists----which weren't generally played on the radio. They'd usually do 'homogenized' versions......which were more 'compatible' with middle class white audiences, and turn them into hits.    Pat Boone was one of the most notorious cover artists.

I personally don't like using the word 'cover' for anything that is less than an attempt to turn some other unplayed version of a song into a 'hit'.