At what step is the difference made between a quesadilla and burrito?

Quesadilla comes from queso, cheese, and that is mostly what goes in there. Maybe some jalapeños or onions, but that's really it.

In a burrito you'd add much more, both volume and variety, for example meat, rice, avocado, cream, cheese, chiles, and beans.

As far as I know the quesadilla goes in the pan on heat, whereas a burrito does not get heated after being wrapped up.

By far the easiest way to make flat quesadillas is just to use two tortillas, like a sandwich. No worries about folding things up that way.

If you want the folded in half or folded in thirds kind, the main things to keep in mind are that you want nice big flexible tortillas, and you don't want to overfill it. That should let you fold it fairly easily, and press it a little flatter with a spatula while it's in the pan without squeezing anything out. If your tortillas aren't terribly flexible, it may help to warm them a bit first. Otherwise they may break when you fold them, which isn't necessarily a problem, but doesn't look quite as nice.

I noticed in comments elsewhere that you mentioned not putting much cheese in either! That's important too - that's what makes it all stick together. Note that it won't stick until it's melted, though, so you still have to put it together right in the first place. You can still put a decent amount of other stuff in (meat, the corn and beans you like, whatever!) but you need enough cheese to balance it out.

Burritos, on the other hand, can take a lot more filling, and they're rolled up from the beginning. If you start out with that much filling, there's no way you're going to get it flat.

The defining feature of a quesadilla, as the name implies, is cheese. If the primary filling isn't cheese, then what you're making isn't a quesadilla, no matter how close you come to a flat semicircle shape.

In other words, to answer the title question, the step where a quesadilla and a burrito diverge is step zero, when you decide what your fillings will be.

• If it's mostly cheese, plus maybe a few things to flavor the cheese, then it'll be a quesadilla even if you totally mangle the folding-up step (or if you omit the folding-up step and use two tortillas). Heck, even if you omit the heating-after-filling step, if the filling is mostly cheese it'll still be a quesadilla, just maybe not a very good one.
• If the filling involves primarily beans and corn, then your dish will almost certainly be considered a burrito, even if you don't manage to wrap the tortilla around the fillings very well, and even if you then heat the tortilla with the fillings. (It's not usual to heat a burrito after the fact like that, but it's been done.)

If you're really interested in the folded-over sort (I prefer this style and quantity), just smash it down with a spatula along the folded edge. If is still unfolding itself, perhaps you are overstuffing the tortilla a little, but you can still force the situation by resting something flat and heavy on top until the shape holds. Usually when the cheese starts to melt, it will stick together by itself anyway.

You're making a half quesadilla. Jefromi is right, the easiest way is to use two whole tortillas, which makes an entire quesadilla.

But if a whole queasdilla is more than you want... I find cutting the tortilla in half before adding the cheese, not folding during cooking, makes the flattest quesadilla.

You can use a knife or kitchen shears.

You kind of know the difference already, but your issues are blurring the line slightly. In a way you're discovering the evolution of the Mexican food types.

Burritos are more cylindrical and have more stuff and less cheese (usually). Quesadillas are mostly cheese and are usually flat and grilled/pressed - like a Mexican grilled cheese or panini. The higher cheese content is supposed to basically glue the thing together. Burritos can use less cheese because their construction is what holds everything together.

I'm thinking the reason your quesadillas are turning into burritos is that you're putting too much stuff in them and maybe folding too late. They should be flat like a double crusted pizza not packed like a calzone. In addition to reducing the amount of stuff, you can try to cut your stuff smaller so that it doesn't create as much bulk and can be more evenly distributed on the cheese. Maybe even only putting it on one side, leaving the other to flip over cleanly.

The idea is to warm a tortilla slightly, then put on the cheese, then extras, then more cheese. You can fold it and press it at this point or put on another warm tortilla. Ideally, the tortilla should still be soft but plenty warm and the cheese only slightly melted[ing] at this point. You might also press it down to just help things stick together better. After it's all folded or covered up, put it back on the hotplate and keep grilling and flipping until both sides begin to brown and stiffen up and the cheese has melted between everything. Normally, I'd use 2 tortillas to avoid creating a burrito or soft taco by accident but if you can't flip it over like a pancake without all the stuff falling out, it's not really living up to the name.

Anyway, that's my 2c.

My quesadillas keep turning into burritos. This happens because I fold the tortilla in half but it doesn't stay so I tuck it in and roll it up by then it becomes a burrito (full and round).

How do I make my quesadillas come out flat?

I am not sure If I understood your problem, but if the tortilla is not "staying" (folded?) you can do a couple of things:

1) pre-heat the tortilla on both sides for a couple of seconds (the pan must already be hot before trying this)

2) wait for a reasonable time for the cheese to melt

3) now you can fold the tortilla and the melted cheese will help the tortilla to stay folded

It really doesn't take that much time in any of these steps, just make sure to pre-heat the pan

If you still have problems, it might be the case that the quality of the tortilla is not good enough. Some low-quality tortillas do not keep the heat for a long time, and start to break apart.

What's the difference?

Typically, a quesadilla is lighter: cheese only (pure quesadilla) or with a couple of fillings (for example you can add meat and make it a "quesataco").

A burrito, as you noted, will be tucked in and typically contain more fillings. Rice should never be one of them!

PS. The advice given by another answer to use two tortillas is incorrect. You do that when attempting to make a sincronizada (you would add ham too to do that).

A small detail some people are missing, burritos are made usually with tortillas made of wheat, and quesadillas tortillas are made of corn.

(Of course you can make a quesadilla with wheat tortillas but traditionally they are made with corn at least that's more common in Mexico)