An End Mill is a type of milling cutter designed to be held by the shank on one end in order for it to cut with the opposite end. The advantage to an End Mill is that, unlike any other type of milling cutter, it is capable of cutting on the periphery, the face or the end of the cutter.
A face mill is a cutter designed for facing as opposed to e.g., creating a pocket (end mills). The cutting edges of face mills are always located along its sides. As such it must always cut in a horizontal direction at a given depth coming from outside the stock.