"Stack" vs. "pile" vs. "heap" of paper

What is the difference between stack, pile or heap of something, let it be for example paper? CS+IT people might tend to use the word heap, because there is a widely known datastructure by that name. So they might say "heap of papers". On the other hand I've heard "pile of papers", "pile of paper". Additionally Google Translate (I know it's not an authority, yet) suggests using "stack of papers".