flatbread is more like a pita without the pocket. It is traditional middle eastern bread which is served with meats, cheeses and olives. They can be topped and used in a variety of ways. It is much thicker than a "wrap" which is a tortilla, which is made of corn or other vegetable bases to give them color and flavor ie: spinach, tomato, etc..
Pizza dough is more of a yeast dough. There are many styles of pizza from deep dish "pan" pizza which Chicago is famous for. Ther is Sicilian style which is a thick but very light crust and neopolitan style which ranges from thin to very thin - depending who makes it.
Flatbread and pizza dough are completely different in texture, taste, and recipe as I do not think flatbread has yeast in it, which is why it is "flat" bread!