If I may hazard a guess, and it's just that, I would guess that the Danish/German elves are equivalent to what the Irish called fairies. They aren't the innocent little creatures who make the leaves frosty, nor the heroes of JRR Tolkien's works, nor the clever Santa's helpers, but nasty, powerful, mean folks that are always up to no good, stealing babies and leaving changlings in their place, kidnapping maidens, etc. This seems to fit with the tone of Goethe's poem better.

BTW, the late Carl Sagan conjectured that the current rash of "alien abduction" stories parallels the "fairy abduction" stories of the middle (or dark?) ages.