A cover song can be different in a very creative way.
Almost all "Be-Bop" era in jazz is out of syrupy love ballads transformed in crazy fast tempo impossible to play tracks... Also, here on NG, all "Game Music" genre is covers or remixes.
People seems to misunderstand terms.
Remix - A remixer uses audio mixing to compose an alternate master recording of a song, adding or subtracting elements, or simply changing the equalization, dynamics, pitch, tempo, playing time, or almost any other aspect of the various musical components.
Because remixes may borrow heavily from an existing piece of music (possibly more than one), the issue of intellectual property becomes a concern.
Cover - a new rendition (performance or recording) of a previously recorded, commercially released song.Cover songs often fall under a mechanical license whereby the cover artist pays a standard royalty to the original artist, and is safe under copyright law even if they do not have any permission from the original artist.
Cover versions of many popular songs have been recorded, sometimes with a radically different style, sometimes virtually indistinguishable from the original.
As a radical change, you should listen to "A Jazz Tribute to the Beatles", then you would agree that covers can be VERY creative.
Also I see here used term of "remix from scratch" which annoys me very much.
A remix is supposed to use some of the original work, so, according to NG rules ALL REMIXES should not be allowed. But "remix from scratch" means actually recreating the song by yourself (from tabs, music sheets, by ear...), so, it's in fact a cover version.