Allright, this is from Webster's collegiate dictionary...

Main Entry: pie
Function: noun
Etymology: Middle English
Date: 14th century
1 : a meat dish baked with biscuit or pastry crust -- compare POTPIE
2 : a dessert consisting of a filling (as of fruit or custard) in a pastry shell or topped with pastry or both

So the "or both" of meaning #2 refute's Rob's Communist notion that all pies must have lids.

Anyway I think this explanation gets at it... (from http://homecooking.about.com/library/weekly/aa073100a.htm)

"Pizza is actually modern Italian for pie. The origin of the term is murky but is said to be derived from an Old Italian word meaning "a point," which later evolved to the Italian word pizzicare, meaning "to pinch or pluck." A Neapolitan dialect of the word first shows up in print in 1000 A.D. in the form of picea or piza, assumably referring to the way the hot pie is plucked from the oven. Early forms of pizza were most likely what we call focaccia today, since the tomato didn't reach Italy until the 16th century, hence no tomato sauce for the pie we know as pizza. The addition of mozzarella cheese (initially made from buffalo milk) did not come about until the 19th century. The standard tomato, basil and mozzarella pizza is first credited to Raffaele Esposito of the Pizzeria di Pietro, who dedicated the creation to Queen Margherita in 1889. The colors nicely coincided with the colors of the Italian flag."

Amazing what Google can do for you.