It was originally called a "Hot Dog Sandwich", "Frankfurter Sandwich" or "sausage sandwich" around the turn of the 20th century. This was the straight-forward

It was originally called a "Hot Dog Sandwich", "Frankfurter Sandwich" or "sausage sandwich" around the turn of the 20th century. This was the straight-forward terminology. Nobody has to go back and prove it from first principles. Dropping "sandwich" from our descriptors over time for convenience didn't change what it is.