To qualify as “a sandwich,” a given food product must, structurally, consist of two (2) exterior pieces that are either separate or mostly separate;
Those pieces must be primarily carbohydrate-based—so, made of bread or bread-like products;
The whole assemblage must have a primarily horizontal orientation (so, sitting flush with a plate rather than perpendicular to it); and
The whole assemblage must be fundamentally portable.
So. Under this definition, a burger is a sandwich. So is an ice cream sandwich. So is an Oreo. So is a grilled cheese. But not a hot dog