The distinction between burger vs. sandwich, from Merriam-Webster:

sand·wich

noun
ˈsan(d)-ˌwich, ˈsam-; dialect ˈsaŋ-
1. a : two or more slices of bread or a split roll having a filling in between
b : one slice of bread covered with food

2: something resembling a sandwich; especially : composite structural material consisting of layers often of high-strength facings bonded to a low strength central core

ham·burg·er

noun ˈham-ˌbər-gər
1 a: ground beef
b: a patty of ground beef

2 a: a sandwich consisting of a patty of hamburger in a split typically round bun

bur·ger

noun ˈbər-gər
1 a: hamburger
2 a: a sandwich similar to a hamburger (i.e tofu burger); —often used in combination

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