Pie and tart are regional (North American versus Western European) terms for essentially the same thing. Some will argue that the pans make the difference (see below), but I don't buy that story.
There are some stylistic differences that appear quite often, but nothing that makes them truly different things:
- Pies tend to be deeper, and have more filling
- Pies tend to be made in a shallow, sloped sided baking pan called a "pie pan; whereas tarts tend to be made with only a ring, or a tart mold which consists of an outer ring with a removable bottom plate. Tart pans or rings tend to have vertical sides, not sloped ones.
- Tarts usually only have a bottom crust
- If the recipe is from France or cooks of a French cooking tradition, it tends to be called a tart; if it is from North America, it tends to be called a pie
- Pies often feature a flakey short crust, or a crumb type crust, whereas tarts often feature a pate sucre type crust, but again this is far from universal
- Pies are usually served from their pan, where tarts are almost never served from their ring—this may be as close to a defining difference as there is!
Both tarts and pies can be made in a variety of sizes, including appetizer or finger food sized, personally sized, or family sized.
In North America, sometimes a turnover (like an empanada or pastie, but hand-sized) which is baked or fried is also sometimes called a pie, hand pie, or even fried pie.
The word pie is also used in England and North America for a class of casseroles made with a top crust, such as shepherd's pie (mashed potato crust), steak and kidney pie, or chicken pot pie.
There is also the gallette which is a pastry made free form without a pan or mold, by making a crust, adding filling, and folding the sides partially over towards the center. This is essentially a free form tart or pie.
Quiches are a savory pie or tart whose filling is based on an egg based custard, often with cheese as well.
Oh... and if it is from New York, made with a yeast raised crust, and covered with cheese and hopefully pepperoni, it is definitely a pie :-)