I would think of "covers" as being the sort of thing that tribute bands do, where they try to sound exactly like the original band, down to the last riff and ornament, and even the vocalist(s) sounding the same.
There is a saying among folk musicians, "make a song your own", i.e. Interpret it in your own way (subject to any copyright considerations, of course, if you are planning on recording it or performing it publicly). Having said that, I am not too keen on those versions that stray too far from the original, e.g. chopping up the song with funky rhythms, changing the timing or basic melody, or just "over-arranging".