Words aren’t isomorphic to their dictionary definitions—words had commonly-accepted meanings long before the existence of dictionaries. Dictionary definitions are just an attempt to come up with a heuristic for identifying things as instances of the defined term, but they’re never perfect—and the common usage is ontologically prior.

If the dictionary definition of sandwich fails to distinguish cakes from sandwiches, it’s just an imperfect definition (like all definitions are)—and we can leave it at that.