My personal definition for (an unqualified) sandwich is that there must be two /isolated/ 'bread' sides surrounding a payload (the 'meat' of the sandwich).

As a quesadilla is often made folded I at first disqualified it; however not /all/ quesadillas are folded. Some are actually made with two individual tortillas. Thus it is close enough to a sandwich to be expressible as a member of that class, while the others that are similarly close are always made with single pieces of bread (cut in the middle) and thus, they are not in fact sandwiches as it is not optional to select different types of bread for the two sides (even though I've /never/ seen anyone do this; it's still /possible/).