This distinction serves primarily to discredit atheism as a movement for public policy. Those vocal atheists are so silly, they talk about facts and reason and science, but they say that god definitely doesn't exist, but they can't prove it. They should just be quiet like the other respectful atheists. After all, if you can't prove it, any position on the subject is equally viable, right?
Asserting the non-existence of a god is the same as asserting the non-existence of Harry Potter or the Loch Ness Monster. These things are supposed to exist within specific parameters. We looked. They're not there. Loch Ness is empty. There is no Hogwarts. There are no gods on top of Mt. Olympus. Are we absolutely, 100% certain that Zeus doesn't exist? No. But we went up Mt. Olympus and he wasn't there. So we're as certain as we need to be to construct a society that assumes his non-existence. The distinction is mostly a distraction to discredit atheist movements. Otherwise it's just a semantic difference for armchair philosophers.
Liberté. Égalité. Fraternité.
Yes, we know you're an atheist, but are you a Catholic atheist or a Protestant atheist?
He who knows the least obeys the best.
In regard to the Abrahamic god and the god of all the religions I am familiar with, I am a positive atheist. In regard to the deistic god I am a negative atheist.
I would also like to remind people that atheism and agnosticism are not mutually exclusive. You can be an agnostic atheist or an agnostic theist.
Extraordinary. We're three pages in and no one's tried to say that atheism is a religion. There really is a god.