What does the word "atheism" actually mean? Does it mean, simply, "lack of a belief in God or gods"? By that definition, babies would be atheists, not to mention cats, trees, and rocks, for they do not have a belief in gods. Or does it mean, "belief that there is no God or gods"? I have seen many debates on the Internet arise, where the people involved were confused about this issue. I hope someone can clarify what the term should mean.
There's no clear answer to this in terms of how the word is actually used. And there's also a dispute in philosophy as how it should be defined. A SEP page proposes that the proper meaning of atheism should be "God does not exist (or, more broadly, the proposition that there are no gods)", as a straightforward propositional negation of theism, but at the same time notes:
While this might seem etymologically bizarre, perhaps a case can be made for the claim that something like (metaphysical) naturalism was originally labeled “atheism” only because of the cultural dominance of non-naturalist forms of theism, not because the view being labeled was nothing more than the denial of theism. On this view, there would have been atheists even if no theists ever existed—they just wouldn’t have been called “atheists”. (Baggini  suggests this line of thought, though his “official” definition is the standard metaphysical one.) Although this definition of “atheism” is a legitimate one, it is often accompanied by fallacious inferences from the (alleged) falsity or probable falsity of atheism (= naturalism) to the truth or probable truth of theism.
Departing even more radically from the norm in philosophy, a few philosophers and quite a few non-philosophers claim that “atheism” shouldn’t be defined as a proposition at all, even if theism is a proposition. Instead, “atheism” should be defined as a psychological state: the state of not believing in the existence of God (or gods). This view was famously proposed by the philosopher Antony Flew and arguably played a role in his (1972) defense of an alleged presumption of “atheism”. The editors of the Oxford Handbook of Atheism (Bullivant & Ruse 2013) also favor this definition and one of them, Stephen Bullivant (2013), defends it on grounds of scholarly utility. His argument is that this definition can best serve as an umbrella term for a wide variety of positions that have been identified with atheism. Scholars can then use adjectives like “strong” and “weak” to develop a taxonomy that differentiates various specific atheisms. Unfortunately, this argument overlooks the fact that, if atheism is defined as a psychological state, then no proposition can count as a form of atheism because a proposition is not a psychological state. This undermines his argument in defense of Flew’s definition; for it implies that what he calls “strong atheism”—the proposition (or belief in the sense of “something believed”) that there is no God—is not really a variety of atheism at all. In short, his proposed “umbrella” term leaves strong atheism out in the rain.
Although Flew’s definition of “atheism” fails as an umbrella term, it is certainly a legitimate definition in the sense that it reports how a significant number of people use the term. Again, there is more than one “correct” definition of “atheism”. The issue for philosophy is which definition is the most useful for scholarly or, more narrowly, philosophical purposes. In other contexts, of course, the issue of how to define “atheism” or “atheist” may look very different. For example, in some contexts the crucial issue may be which definition of “atheist” (as opposed to “atheism”) is the most useful politically, especially in light of the bigotry that those who identify as atheists face. [...]
Wikipedia discusses the contrast you inquire about under implicit and explicit atheism, which are apparently terms introduced by George H. Smith.
In George H. Smith's [1974 or 1979] Atheism: The Case Against God, "implicit atheism" is defined as "the absence of theistic belief without a conscious rejection of it", while "explicit atheism" is "the absence of theistic belief due to a conscious rejection of it".
Smith doesn't seem to quite have fit the bill for an academic philosopher, so e.g. the SEP page seems to ignore him, or at least his exact terminological proposal. And in fact so does IEP which prefers to use Flew's terms for roughly the same notions:
It has come to be widely accepted that to be an atheist is to affirm the non-existence of God. Anthony Flew (1984) called this positive atheism, whereas to lack a belief that God or gods exist is to be a negative atheist.
Smith's book did get at least one review in an academic-philosophy journal in 1982. Flew apparently introduced his terms in a 1976 article; Wikipedia has a separate page discussing these. Apparently Dawkins rejected or at least avoided the dichotomy preferring to use a graded scale instead with total conscious rejection at one end. (In this regard, finer grained distinctions can be made in terms what is actually rejected. Both SEP and IEP devote much more space to this issue, under the terms local vs global and respectively narrow vs wide atheism. SEP also discusses two kinds/degrees of agnosticism, psychological and epistemological; the latter is the stronger kind of claim that the existence of God can neither be proven or disproven, so the proposition is neither true nor false, in contrast to mere psychological agnosticism where one simply doesn't personally claim to know.)
It’s of course important to check definitions with the person you intend interacting with, but for me, atheism is the opposite of theism:
Theism - the belief in a god, or gods.
Atheism (a-theism) - the lack of a belief in a god or gods. There are some who go further and state with some certainty that “there is no god” and in doing so adopt a burden of proof. I personally don’t; if sufficient evidence is presented I’d be perfectly prepared to change my mind, and I don’t know with any certainty that there isn’t a god, but for now, I lack belief. And to pick up on a point made in another answer, yes - all babies are atheistic: how could they be otherwise? I reject the notion that to be an atheist one must first have been a theist. I’ve never been a Scientologist for instance, yet I’m perfectly happy to believe it’s a made up, quasi religious, money making scam. Neither have I been a believer in Thor, or Vishnu, or Jehovah, or Allah. I don’t need to have been, to claim a lack of belief.