"Pie" vs "Tart"?

Generally speaking, a pie refers to a pastry covered with a lid, like a typical apple pie. A tart is open topped, like a quiche, or a French tartes aux pommes.

However, there are exceptions to this: many pies will be open topped too. Usually this is a matter of depth: the deeper it is, the more likely it is to be called a pie rather than a tart.

Regional variations also apply.

It's the shape. A tart is baked in a shallow dish with straight sides; a pie dish is deeper, and has sloping sides. At least, that's the way it is in the US.