You do mean the jacket itself, don't you?
Working purely from memory:
Used to be that jackets were made almost exclusively of what is known as "gilding metal," an alloy of copper and tin, which was developed as follows:
A long time ago the French used to add tin flakes to their artillery shell powders to eliminate the copper fouling caused by the pure copper rotating bands on their shells.
Sometime later, when copper jackets for small arms became commonplace, the copper fouling became really severe with the higher velocites attained in these small arms, especially near the muzzle, where the bullet was moving fastest.
The military started to add tin flakes to small arms powders to alleviate the fouling problem. To differentiate these from the regular powders, a "1/2" was added to the powder designation.
For one of the 1920s National Matches, Col Townsend Whelen developed a copper jacketed bullet which was plated with tin.
This was called "Tin-Can" ammunition, and apparently shot very accurately, and almost completely eliminated the fouling problem, but was quickly withdrawn from the matches because despite explicit instructions to the contrary competitors insisted on dipping the bullets in grease for lubrication. This practice was known to increase pressures disastrously and several Match rifles were "broken" because of the grease on the bullets.
After that, I believe it was Winchester-Western who discovered that the same effect would be obtained by alloying the copper jacket material with tin directly. This product was called Lubaloy (for "lubricating alloy", also known as gilding metal), and could be used with either full-metal jacked bullets or soft-point hunting hunting bullets, the advantage being the reduction in jacket material fouling, not any other magical property of the material.
Nowadays, the jackets of FMJs can be made from very soft ("mild") steel, but are usually "copper-washed," meaning lightly plated with copper.
Variations in "hardness" may be due to either the thickness or exact composition of the gilding metal jacket material or to the annealing methods and thickness of steel-jacketed bullets.
Whether they are FMJs or hollow-points or soft-points.
Note that even steel-cored bullets (as opposed to the steel jackets) have a thin layer of lead between the jacket itself and the steel core to allow the bullet to be engraved by the rifling.
Again, strictly from memory. Anyone can feel free to correct or add to this story of bullet jacket materials.