I would say a quiche /ˈkiːʃ/ requires eggs whereas a tart doesn’t (necessarily), and I have no idea what a key-tch-zah is, we don’t have them in the UK. A quiche is a type of tart though, yes.
No judgement but here in the UK this is more like what we’d call a flan than a pizza or a pie. So instead of arguing about pizzas and pies, why not embrace a third category?