Queso Oaxaca, called quesillo in much of Mexico, is the stretchy one. It is a white, stringy cow's-milk cheese made by the pasta-filata method, the same family as mozzarella, in which the curd is heated and pulled into long elastic ribbons and then wound into a ball you unspool by hand. That construction is the whole identity. Where the other Mexican melters flow into a creamy pool, quesillo pulls into long, milky strings, and that pull is exactly what a quesadilla is built around. Its job in a sandwich or folded tortilla is stretch and bind at once: it ropes the fillings to the wrapper and gives the long cheese strands that define the bite, while staying mild and milky enough not to fight the al pastor, the squash blossom, or the rajas it is melted with.
Working it well starts before the heat. The ball is unwound into thin shreds rather than chopped into chunks, because the fibers melt and stretch along their length; torn fine, it melts fast and ropes cleanly on the comal. Brought to moderate temperature it goes glossy and elastic and pulls a long, clean string, holding a folded tortilla shut and stringing satisfyingly when you pull it apart. The failure modes are specific to a pull-cheese: under heat held too long it tightens and squeaks and can turn chewy and rubbery while shedding a little fat; left in a thick wad rather than shredded it melts unevenly, gooey at the center and tough at the edges. Its mildness is functional, a faint salty-milky base that carries other flavors rather than competing, so it reads as texture first and flavor second.
It substitutes for low-moisture mozzarella and is the default cheese for quesadillas, tlayudas, and stringy melts across the country, with quality ranging from bouncy industrial balls to softer hand-pulled artisan ones. How its long pull contrasts with the smooth flow of asadero, the buttery Chihuahua melter, and the bland manchego mexicano turns on exactly this stretch behavior, and that comparison deserves its own article rather than being crowded in here.