So, based on people's reactions and explanations, can we assume that "sandwich" is a term that has a different sort of connotation based on region? American English tends to lump a lot of different things under one umbrella, and it looks like "sandwich" is no exception. For what it's worth, "burger" can be used to describe any sort of filling between two vertical buns. Hot dogs seem to be an anomaly at first glance, but once you look into the regional variants, they sort of wind up being their own category.