Technically it's a grilled cheese sandwich, right?
But getting into technicalities:
According to Merriam-Webster, a quesadilla is a sandwich if you classify a tortilla as bread. A sandwich is defined as "two or more slices of bread or a split roll having a filling in between" or "one slice of bread covered with food". A quesadilla is made with a tortilla and cheese, but the tortilla does not contain a leavening agent and therefore cannot be considered bread.