EPP, AKA English paper piecing, you use the same paper template and fold your fabric over it. Templates can be diamonds, hexagons, etc.. You then hand baste the fabric over the whole template. Later you would usually hand-sew the blocks together.
Paper piecing (PP), is where you have a pattern of a block printed on a piece of paper. The block is divided into numbers and you place you fabric and sew on the pattern in the order of numbers, starting with #1. Kind of like paint-by-numbers.
So, as sJens said, one is sewn by hand and the other is sewn by machine.