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:
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.
The original European Kugelhopf (aka Gugelhupf) pan, which dates back centuries, is a mold pan designed to look like a Medieval hood or bonnet (Think Shakespeare or Henry VIII headwear designs) that was made of cast iron. It is heavy.
The original Bundt was designed at the request of European immigrants in America by Nordic Ware around 1950's to duplicate the Gugelhupf design in a lighter pan. It was a popular cake to these immigrants during Holidays and Weddings. Once it caught on in popularity new designs were added as we see in today's Bundt pans.
Lastly, a Rodon pan is any variation on that original Bundt pan or a Tube pan, as it is simply a "Ring Cake", whereas the Gugelhupf was vertical but slanted or "twisted." It was the only cake that followed a traditional design. The pictures above are not really accurate if your going for true design. All 3 would be a Bundt, the middle would be a Gugelhupf and all 3 could be used to make a Rodon, though for standard baking purposes all 3 are Bundt pans. Also Rodon is really just about the recipe and not the design (save for the ring shape), so any Bundt or Tube pan is acceptable. Gugelhupf is a yeast cake, whereas Rodon is not. Bundt is simply the pan variety, not a specific recipe.
The Gugelhoph is, according to my cake-baker wife, the ancestor of the Bundt. The main difference is that it's slightly shallower than the Bundt, and its flutings are at an angle, producing a swirl effect, whereas Bundt flutings are parallel to the tube.
Rodon fought Ultraman in Episode 19.
