I searches around a bit and found that the same manufacturer often offers forms under all three names, so I don't think this is a synonym. Also, I found a forum thread (in German) suggesting that there is a difference, but not explaining the difference.
So, what is the difference between the three pans? Is it the proportions (height vs diameter vs inner cylinder diameter)
Gugelhupf:
Rodon:
Bund:
Best Answer
Wikipedia to the rescue.
Gugelhupf is the generic german name for Bundt which is how it's known in the USA.
Rödön is a village in Sweden where they claim to have invented the 'sandwich cake' (even though this cake doesn't seem to resemble the Bundt at all).
If you read the article about Bundt, you'll see that the designer took elements of Scandinavian pan designs, so there might be a relationship with Rödön.
In Dutch, these are called 'turban pastries' for the shape of the pan. The German word Gugel means hood.