A full quesadilla is made with two tortillas that hold a layer of cheese between them. Difference between barbacoa and carnitas half is a single tortilla that has been filled with cheese and folded into a half-moon shape.
The quesadilla has its origins in colonial Mexico. The quesadilla as a dish has changed and evolved over many years as people have experimented with different variations of it. In the central and southern regions of Mexico, a quesadilla is a flat circle of cooked corn masa, called a tortilla, warmed to soften it enough to be folded in half, and then filled. Mexican quesadillas are traditionally cooked on a comal, which is also used to prepare tortillas.