A cover typically sounds close to the original, since it's meant to be the same piece of music just performed by a different artist. On the other hand a remix can sound completely different from its source, but should include some of the original instruments or vocals. Case in point:
Original
https://www.youtube.com/watch?v=aFm87ncj-Xc
Remix
https://www.youtube.com/watch?v=yWbTQb6mmbg