Without fragmentation, isn't it just going to fly off in one direction with very little damage in any other direction?

All grenades have a casing the "fragments" when they go off, but some use thicker, heavier, scored metal casings to maximize the anti-personel effects of the resulting shrapnel. If you don't want shrapnel, then you make the casing light and arrange for it to break into fewer pieces. So grenades designed to produce more, heavier, sharper fragments are called fragmentation grenades.