Americans consider hamburgers to be a type of sandwich. It can be confusing to people from other countries who don't consider meat in a bun (as opposed to meat between slices of bread) to be a a sandwich.
Of course not. I’ve been saying for this whole conversation that it’s simply odd, when X is a subset of Y, to use language that implies that X and Y are disjoint sets.
I kind of get what you mean, but those are very different.