I don't think that is precisely accurate -- to say that an unbeliever of a particular system is an atheist of that system. At least as I understand the term, it is absolute: a-theism = without a theism. That doesn't allow room for selection or preferences.

Just as the opposite of atheism -- theism -- does not allow for unbelief.

I believe there are plenty of terms other than atheism to describe the various states of non-belief that a believer may have. These maybe heresy, apostasy, etc all of the way to antidiestablishmentarianism.

Are Dawkins, Hitchens and other atheists all of the same quality or measure of unbelief? I don't think so. My Dad (for example) was an atheist but I'd call him a sort of laissez-faire atheist. I have a sister who is a casual or unfaithful atheist -- dabbles in religious exercise every decade or so. In my own peculiar case, I step over the line into superstitious agnosticism -- Proof would set me free from a belief that tehre is more to life and death, than life and death.