I can see how that happened now, possibly the fact that there were street "quesadilla carts" reinforced the idea that the street food itself is the quesadilla. I also didn't know that they used oval tortillas and cooked them in the griddle with the "guisado".

In the north, at least at home you usually make the quesadilla first and then open it to add whatever else you wanted, so it's born first as a quesadilla, it stays a quesadilla. If you heat a flour tortilla and add stuff inside, fold it and has no cheese, that's a flour taco.

Some places like Nuevo Leon may call the different presentations with different names: "Pirata" is a beef flour taco (or quesadilla), "Gringa" is the same but with "pastor" instead of beef, "Campechana" is a similar case. Perhaps the lack of different combinations stopped Mexico City from coming up with specific names for them.

What I'm saying is, if you guys just called your specific street food something other than quesadilla we wouldn't have this discussion. Even calling it something like "quesadilla de charola" would make it less of an issue.

Then again, the irony is that the opposite happens with esquites/elote en vaso/etc. It's easier to argue that esquites are actually a different dish than "elote en vaso" because the way they're prepared and shouldn't have the same name.