Hah! When T and I were discussing this last night, after I posted this, he also consulted the great god Wikipedia and pointed me to the exact same article.

Thus hamburgers and "subs", for example, are called "sandwiches" in the United States, although not in the midwest, south or western states or most other English-speaking countries

I agree on hamburgers in the West and Midwest (my two main points of linguistic reference) but not on "subs" -- we call those sandwiches. When I go to Subway et al., I'm not geting a "submarine" (or any of the other regionalisms used for this food item), I'm getting a sandwich, or maybe a deli sandwich.

since they are not made with slices of bread from a loaf).

Ah, but on Sunday evening, I had a hamburger for dinner. The hamburger was not on a bun but rather on slices of sourdough bread. Was that a burger? Or was it a sandwich.

All kinds of linguistic permutations here...