A bullet is the metal object that is fired out of a gun when its trigger is pulled. Without bullets, a gun is harmless.
If someone talks about ammunition for a gun, they're talking about bullets. A bullet doesn't usually contain explosives but does its damage by penetrating whatever — or whomever — it hits. The Middle French source of bullet is boulette, "cannonball" or "small ball," from boule, "a ball," with its Latin root bulla, "round thing." To "bite the bullet" means to withstand an unpleasant but necessary situation, from the (possibly fictitious) practice of patients biting bullets during painful operations.