Actually Rrhain, I think the distinction you're making pertains more to the difference between so-called "strong atheist" (active denial and/or active anti-theism) and "weak atheist" (manifesting a lack of belief as you mention). Most of the people I know who self-identify as atheists fall somewhere on a spectrum between those two distinctions - and may even elide into agnosticism or fall on multiple places on the "scale" depending on which particular deity or aspect of theism is in question (positive an anthropomorphic entity doesn't exist, less positive or even agnostic about a more deist interpretation). Since we're discussing personal philosophy and self-identification, it isn't surprising that easily delimited categories don't exist.
I personally probably fall close to DrBill's atheism/anti-theism stance. Whether that refutes your statement that this brand of atheism
...isn't actually followed by most atheists. It isn't that they don't believe. It is that they have no belief.
That is, atheists don't "believe there is no god." Instead, they "have no belief in god."
or not I have no way of judging. I neither know "most atheists" well enough to make the call nor do I believe that there is some over-arching atheist philosophy that could be considered definitive and hence provide a standard by which all atheists can be classified.