As far as regular real-life firearms are concerned, the material of the bullet affects penetration and fragmentation (here: armor penetration and 'health damage'), while the impact power (damage) is a property of the cartridge itself, for the most part. So a .44 magnum revolver round will (in almost all cases) have more raw 'damage' (due to high kinetic energy), even though it's made of soft lead, while a 5.7mm (a modern armor piercing pistol round) will rip through armor, but leave comparatively smaller wounds. I don't want to turn this topics into a lecture on firearm mechanics so if you want more detail you can read up on the internet or drop me a PM.
TL;DR - yes, it works the way it's supposed to.