It's confusing, but think of the 700c designation like 2X4s from the lumberyard: it's a nominal size. The actual size is 1-1/2"X3-1/2", but everyone calls it a 2X4.

Some tires actually do measure 700mm (not 'c' like centimeters...oh well), but since it's only a nominal diameter, it changes with the tire width.

For instance, my Surly Pugsley has a nominal 26" rim (559 ISO) that likely would measure 26" in height with a 2" tire, but since the tire is 3.7" wide, it measures an actual 29" in diameter. Were I to put a 1" road tire made for the same 26"/559 ISO rim on there, overall diameter would actually measure out to a little over 24". Crazy, I know.

Sheldon has a good article about it here.