In Spain, tortilla is generic for omelette. A tortilla de espana (sorry, no tilda on this board) aka tortilla de papas is incredibly typical of bar and home food. In Spain, tortillas are made "pancake" style, by sliding the half cooked omelette out of the pan onto a plate, then inverting it back into the pan. In other words, it's cooked in a pan on top of the stove and not in an oven. Tortillas are usually more fluffy than custard-like. In Spain, tortilla can refer to pancake as well (also panqueque and tortita).
In Mexico, the term "tortilla" usually does apply to unleavened flat bread. But also means omelette, pancake and pie. The commonality is "flat and round." Here, in the US of A, "Neighbors to the North" as we are, we usually only hear the term applied to the bread. FWIW, almost all Mexican tortillas are made from corn, i.e., tortillas de maiz. Flour tortillas, tortillas de harina are a custom which began here in el Norte. Chicanos and Mexicanos mostly reserve them for burritos. For whatever reason gabachos, a term most gabachos confuse with gringos, seem to prefer tortillas de harina generally. I'm not favoring one or the other, it's purely personal preference and not a matter of virture. That's just how the ethnic groups trend.
A frittata is partially cooked on the stove top, and partly in the oven. The texture falls somewhere between airy and rich.
A quiche is cooked entirely in the stove. It is a custard and not an omelette.
Hope this helps,