Once upon a time, I was listening to a CD containing Drum N Bass "remixes" of Art of Noise songs (previously mentioned in this list). I didn't buy the CD 1. because I was too cheap 2. because I could barely recognize Art of Noise in the "remixes". So your first statement about "recognizable elements" seems to be the most universal one. Now I pose a similar question - it seems sometimes Remixes and Covers overlap. Take for example Red Hot Chili Peppers cover of Love Rollercoaster. That doesn't sound very much like the original! But I wouldn't call it a remix, I still call it a cover. Then there's a Cure cover of a Jemi Hendrix song that I can barely remember because they just totally made a new song out of it.... Cover or remix? Of course a person/band cannot do a "cover" of their own stuff, right? So is that horrible Tom Craft remix also a cover? Just more random thoughts and hopefully I haven't misdefined any words this time.