Existential Comics

Having a specific name for a category of objects within another category does not exclude it from the first though. You don't usually say "let's get an animal" when you're talking about getting a dog. It doesn't make dogs less of an animal either.

Yes, but things still routinely get excluded from categories whose definition they technically fit, for cultural or historical reasons. Hot dogs not being typically thought of as sandwiches is a pretty good example.

But, even without the bread, a hotdog is still a hotdog, so the quandry still exists.

Indeed, a hot dog is a type of sausage. The fact that it is typically served on a bun is no different than the fact spaghetti is typically served on a plate.