What's a cover? In my mind, it's someone doing another version of someone else's song; and by "someone else's song," I mean whoever made THE definitive version. F'rinstance, there are tons of Chuck Berry "covers," because nobody does Chuck Berry like Chuck Berry. His version of "Maybellene" is THE definitive version.
But you take a song like Dave Brubeck's "In Your Own Sweet Way," and opinions can diverge widely about who made the definitive version. Was it Dave himself? Or was it Miles? Or was it Bill Evans on How My Heart Sings? In each of those instances, it's a brand new statement. In the former example, it's an artist paying tribute to or trying to ride the coattails of the artist who set the standard.
Does that make sense? I think I may have painted myself into a coroner.