On the nomenclature, in the 1930's the army went from using the year as a model name to using M1, M2, M3, etc. So every major item thereafter was given an M number. The rifle was the M1; the carbine the M1 or M2 or M3; ball ammuntion was M1, M2, etc.. Trucks were M1, M2, etc. Tanks were M1, M2, M3, etc. (The famous Sherman was the M4.)
So the correct name would be Cartridge, Caliber .30., Ball, M2 or Cartridge, Calliber .30, Armor Piercing, M2. Two different cartridges, but both the second version adopted after the nomenclature change.
It is interesting how AP bullets pentrate. When a bullet strikes a solid object that stops it, its remaining energy is instantly transformed into heat. In the case of an AP bullet striking steel, that heat melts the steel in a small area. If the plate is thin enough, it will be melted or at least softened all the way through. This allows the carbide core, which won't melt, to penetrate. If the plate is too thick, the core will either bounce off or remain stuck when the molten steel "freezes". It was common to see AP bullet cores sticking out of the steel of tank armor; the cores did not penetrate because the armor was too thick for the heat to melt it through, and the cores were trapped when the steel solidified.
(Think about the above and you will figure out why a barrel bursts when a fast moving bullet hits an obstruction.)
Jim