I think the parallel many draw is that atheism is taking a position of certainty on the question of a God. And that certainty is based largely on personal belief as any evidence for such a question will inherently be weak.

To me agnosticism would be more the absence of religion, because the absence of religion doesn't imply any particular opinion on the existence or not of a God. One can believe there might be a God without embracing any religion.

The idea that someone can be without “religion” is very odd. The word “religion” is generally worthless as used, as for most people, this is merely some vague sense of what was called “religion” in their particular experience. But a coherent common characteristic, as it were, is that it is a worldview with a highest good. Everyone has some kind of worldview and some notion of a hierarchy of goods, usually something absorbed from their environment.

So it is pointless to speak of whether you are “religious”. It makes more sense to ask how you are religious. It is far more interesting to discuss the merits of your religion or other religions than to go around pretending you don’t have one.

The first isn't atheism, it is agnostic - no religion and not looking for one, but open to it if you can convince them your religion is right (which you can't because they are not interested in the topic)

Atheism is defined as the absence of belief which is essentially what OP said.

The fact that we are open to changing our mind if theoretically presented with strong evidence does not make us agnostic.

You’d probably also accept that sun is made of cheese if presented strong enough evidence but don’t call yourself agnostic about the topic given your current knowledge.

Atheism is the position that God does not exist. An atheist is someone who therefore says “I believe that there is no God.”

It is not a mere lack of belief, as agnostics can be said to lack belief in God as well. People who are simply ignorant of God also lack a proper belief in God, but this is not atheism, only ignorance. They simply have not come to terms with the subject and therefore have no position on the matter. An atheist does, however unsophisticated it may be.

This view that atheism is simply a lack of belief in God is common among the intellectually challenged New Atheist crowd and would have been ridiculous to the much more intellectually substantive atheists of old, like Neitzsche (who, btw, while an atheist, found it a horrifying thing; the other classic atheists could be described as world-weary rather than insipid, parochial, middle class triumphant).

For someone concerned with the lack of intellectual seriousness of the New Atheist movement, you seem especially committed to ontological realism. Is there some compelling argument I've missed?

That aside, "atheism" can obviously mean both things—with regard to a belief or the endorsement of an "existence" proposition. In the case of atheism/theism, the belief part plays a substantial role—it distinguishes between B(~p) and ~B(p), the strong and weak positions, respectively.

There are other ways besides ignorance or agnosticism to arrive at ~B. For example, if my view is that ontological claims can't be propositions, then obviously I can't have beliefs about them one way or another. Or I could reject all supernatural claims out of hand. Why would you insist that one take a firm position on whether "God" specifically "exists" or not? Isn't atheism just a consequence of these views?

To put it plainly, logical consequences of other views can make one an atheist just as much as rejecting p outright. One needn't explicitly endorse or reject every mystical metaphysical claim out there. That would be a bit silly, just as it's a bit silly that we've inherited a special word for "atheism" in the first place.

In practice though, unless you're in the Richard Dawkins camp, it's a distinction without really a difference.

The Richard Dawkins camp is pretty large (or maybe just vocal?) on the internet though and so the difference is important.

I vote vocal.