Gun lube is used for lubing guns.
Bullet lube is used for both sizing and to minimize leading of lead bullets.
Case lube is used to keep brass from sticking in reloading dies.
The "wax" rings in your lead bullets are a form of bullet lube that's melted into place when the bullet is swaged/sized by the maker. If you were casting your own bullets you might do this yourself, or you might find that too difficult, so you'd use something like Lee Liquid Alox (LLA).
I've shot quite a few lead rounds like you describe, both rifle and pistol, without having to do any additional lubing of bullets. Some folks put some additional LLA on their bullets to minimize leading. I've never found this necessary, and find that LLA itself is such a sticky mess I'd almost rather deal with the leading. But then, I've never experienced excessive leading in any of my guns using the pre-lubed bullets, either.
The foregoing is my opinion and collection of stuff I've picked up after loading for a couple of years. If I'm wrong someone will be along shortly to correct me.
-- Sam