Not to split hairs, but I believe there is a distinct difference between a burger and sandwich -- and it's not a dialectal one. A burger always has a patty (which isn't just meat, but a piece of flattened ground up meat) whereas a sandwich does not. The burger patty is what makes a burger a burger and not a sandwich.
That's why you'll hear the term chicken sandwiches (because they don't contain patties), but you'll never hear burgers ever being called "beef" sandwiches. (Beef sandwiches exist -- like roast beef sandwiches, beef-on-weck, Italian beef, pastrami sandwiches, etc. -- these contain forms of beef that are not burger patties). Beef burgers and beef sandwiches are different things.
Similarly, chicken sandwiches ≠ chicken burgers. They're different things. The latter always has a (chicken) patty. The former almost always doesn't.
McDonald's and most other fast-food places are actually pretty consistent with their burger vs sandwich terminology and don't really mix them up.
It sounds like your concept of "sandwich" is ontologically incoherent. What kinds of generalizations apply to all or most sandwiches but not to a patty between slices of bread? We have "sandwiches don't contain patties", of course; but is there anything else? It sounds sort of like defining "Indian" to mean anyone from India who isn't from Goa, "British" to mean anyone from Great Britain who isn't from Cornwall, or "murder" to mean any event of one person killing another except when the first person is named Derek.
Such ontologically incoherent definitions are obstacles to clear reasoning (though less seriously than eargrayish definitions like defining "murder" to mean either one person killing another or stepping on the shadow of the King). Is there a reason your proposed definition of "sandwich" is not among them?
Since you mention India, would you consider curry to be a kind of soup? I believe the relationship is similar to that of burgers and sandwiches.
A curry is "just" a soup with spices. But if you walked into a restaurant and ordered "soup of the day" and got a vindaloo, you might feel deceived. If the waiter assured you that a vindaloo is ontologically a soup, I doubt that would be much consolation.
Sometimes in language, if you use a general term (A), when a more specific term exists (B subset A), then using that general term A carries the meaning A\B, because if you had meant B you would have said B instead.
It's an interesting question! I normally think of a curry as being a sauce placed on some solid food, while a soup is a liquid food with perhaps some solid chunks floating in it; but that's really just a difference in how it's plated and how much sauce you use; it doesn't make much difference to the flavor.
> In the past all observed emeralds have been green. Do those observations provide any more support for the generalization that all emeralds are green than they do for the generalization that all emeralds are grue (green if observed before now; blue if observed later); or do they provide any more support for the prediction that the next emerald observed will be green than for the prediction that the next emerald observed will be grue (i.e., blue)? Almost everyone agrees that it would be irrational to have prior probabilities that were indifferent between green and grue, and thus made predictions of greenness no more probable than predictions of grueness. But there is no generally agreed upon explanation of this constraint.
(This is somewhat mineralogically naive, because emeralds are just green beryls; a beryl that was blue would be called an "aquamarine" or "maxixe," not an "emerald," because greenness is part of the mineralogical definition of "emerald." But it's straightforward to change the riddle to refer to, for example, grass. The grass has always been grue; should we expect it to still be grue tomorrow?)
Fortunately, as Wikipedia explains, most people do not share the illogical convention you are advocating, though presumably most of the people you know do.
(...please God don't let him ask me about hotdogs...)
That's why you'll hear the term chicken sandwiches (because they don't contain patties), but you'll never hear burgers ever being called "beef" sandwiches. (Beef sandwiches exist -- like roast beef sandwiches, beef-on-weck, Italian beef, pastrami sandwiches, etc. -- these contain forms of beef that are not burger patties). Beef burgers and beef sandwiches are different things.
Similarly, chicken sandwiches ≠ chicken burgers. They're different things. The latter always has a (chicken) patty. The former almost always doesn't.
McDonald's and most other fast-food places are actually pretty consistent with their burger vs sandwich terminology and don't really mix them up.
https://www.mcdonalds.com/us/en-us/full-menu/burgers.html
https://www.bk.com/menu
https://www.chick-fil-a.com/menu
Source: paid my dues and eaten too many burgers and sandwiches to gain this useless knowledge.