Ammunition terms can get confusing – this will straighten things out.
Cartridge aka Round: The whole enchilada – a metallic package containing all 4 components - casing, primer, powder (propellant) and bullet.
Bullet: The projectile. Most commonly made out of copper jacketed lead.
Shell: Applies to shotguns in the firearms world (but also artillery). The entire cartridge of primer, powder, wad, shot and hull.