Fine = You only get 1 ray per pixel

Super Fine = you get control of Rays per pixel. Default is 16 but you can go all the way up to 256 More rays equals soft lights and shadows or less banding in lights or shadow renders. If you are doing a Sword in the Stone type render with visible light you might notice bands in the light with fine rendering. It also hapens in clouds or other objects with partial transparency. Go to superfine and add rays per pixel till it goes away.