Though the word "bullet" is often used incorrectly in colloquial language to refer to a cartridge round, a bullet is not a cartridge but rather a component of one. A round of ammunition cartridge is a combination package of the bullet (which is the projectile), the case (which holds everything together), the propellant (which provide majority of the energy to launch the projectile) and the primer (which ignites the propellant). This use of the term "bullet" when intending to describe a cartridge often leads to confusion when the components of a cartridge are specifically referred to.
According to this Wiki article, the word bullet only refers to part 1. The whole is called "a cartridge round" or "A round of ammunition cartridge". But those terms sound more technical and I guess they probably would not be used in day-to-day conversations.
So, what's the correct word to describe the whole thing(including part 1,2,3,4,5)? Is it just "bullet"?