from a topological perspective, wraps and tacos are two different beasts.
in a wrap, the bread completely surrounds (and encloses) the other ingredients, so theres a 2-dimensional hole involved (which basically means the inside is hollow).
in a taco, no such wholes are present.
you can also distinguish sandwiches from tacos and wraps (since sandwiches involve two pieces of bread, like you said). but unfortunately, you can’t topologically distinguish a burger from a sandwich
A chicken sandwich is a sandwich when the chicken meat is between two slices of bread cut from a bigger loaf. It's a chicken burger when it's between two halves of a bun.
And as you said, hamburger derives from the German city of Hamburg, so Germans, not Americans, have the authority here.🤪
But tacos traditionally are more like wraps by your definition, with the exception being hard/crunchy tacos which are on what i would technically call a chip, this making crunchy tacos just portable nachos
Additionally walking tacos are supported by a chip bag, making them neither a taco nor nachos.
Hmm, what of rolls? Ciabatta, Kaiser rolls? Even croissants? By this definition it seems they'd be burgers, since rolls are cut in half. But then my roast beef sandwich is a lying, cold, sad burger
You have weird Ciabattas if you think that Ciabatta is a kind of bun and not a bigger loaf. Croissants are pastry. And yes, burgers made with Kaiser rolls are totally burgers: