Remixes aren't strictly made only of original parts, but the main point is that it's the original stuff and there's little or no content added from other songs (though there could be new content added).
"remix" and "mashup" do tend to be used interchangably but I believe my definitions of them are technically correct.
Rob Zombie - Spookshow Baby (original)
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Rob Zombie - Spookshow Baby (remix, I think done with the help of Rammstein)
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