Please avoid using these terms improperly. The improper use of this terminology makes the person speaking or writing sound like a socialist or a liberal Democrat! You don’t want to sound like one of those fools do you? Of course not!
This is really simple. A bullet is a projectile! It is the object that comes out of the cartridge case when the primer is struck and activates the propellant inside the cartridge case. As it clears the case the powder gasses expand rapidly, causing the brass case to seal against the throat of the chamber and seal the powder gasses in the chamber and bore until the bullet exits the barrel at the muzzle end.
The cartridge is the entire contraption, the cartridge case, the primer, the propellant, and the bullet all in one unit! It is a cartridge, not a bullet! The cartridge is not a projectile. The cartridge is not a bullet!
Calling cartridges bullets makes one sound like a liberal! How did this mix up occur? It is really pretty simple. Most of the decent older western movies knew the difference. When someone in one of them ran emptied his pistol, he often said he was out of bullets. Was he wrong, that depends, but probably not. If you look at those old films, you will notice that most of the characters carried revolvers requiring the loading of the components in the weapon separately. A Colt army or navy or dragoon had to be loaded with each of the components minus the case. When someone ran out of bullets, they were literally out of bullets. Rifles, and handguns such as Colt’s famous Peacemaker and the Spencer and Henry rifles were cartridge rifles.
Try not to sound like a liberal! You don’t want to do that! A bullet is a projectile, not the entire cartridge!