Okay, so to settle this long standing war on words, I just looked up the definition of a hot dog for the benefit of our studio audience.
What defines a hot dog is the wiener itself, not the bun. As long as the meat filling is either a sausage or looks like a sausage, then it is called a hot dog AS LONG AS that wiener is then placed within a suitable bun or other bread wrapping.
The bun however is typically a split bun designed for this purpose, but doesn't have to be a bun at all, as long as the wiener is placed within some kind of bread unit so that the wiener can be held in the hand and eaten.
That bread unit can also be a slice of bread wrapped around the wiener for the entire thing to be called a 'hot dog'.
If that wiener is eaten by itself without a bread wrapping of some kind, it is simply called a wiener, not a hot dog.