There are at least four broad, often overlapping, meanings someone could intend with the word atheist.
Some argue that there is a preponderance of reasons against believing in personal/interventionist gods that affect human history and thus they are atheists in the sense that they affirmatively disbelieve in all gods or, even, claim to know that there are no such gods. This is my position and I defend it here.
Someone could go further and reject even all deistic conceptions of gods. I like to use the coinage “adeist” for that position, in order to distinguish it from the rejection of the strictly personal gods that theism claims exist. In other words, as far as I’m concerned, if you reject the personal and interventionist characteristics of gods or “God”, then you are, in socially and religiously relevant respects, effectively an atheist. Even if you continue adhering to religious practices and identities, unless you believe God or gods are personal and interact with the world with distinct personality and efficacy, you are denying the core of what is meant by theism and are an atheist. You might also be some sort of a deist, consistent with being an atheist. I think once we clarify that these are distinct concepts they’re actually reconcilable.
But, most people will only allow that you are an atheist if you reject both theism and deism. I think it’s better to define atheism as the opposite of theism and adeism as the opposite of deism. I think that is more clarifying than to make atheism mean the rejection of both theism and deism, when they’re too distinguishable questions. (See my post It’s Atheism, Not Adeism.) But, regardless, I obviously agree that someone who rejects both theism and deism is an atheist.
Another way you can be an atheist is by taking an epistemological stance that you refuse to either believe or disbelieve in gods but simply to default to “lack of belief”. Essentially in such a case you are saying that either you yourself or all people generally have insufficient information to make any explicit affirmations or denials related to the existence of gods. This might be because you are an ignostic atheist. In that case you think the concepts of God and gods are too poorly or inconsistently developed that you don’t even know what it would mean to say that there was or was not a God or gods, and so by default you don’t believe since you’re unclear what you’re even being asked to believe.
Or you could be an agnostic who thinks that there is a paucity of good evidence for the existence of gods at present and/or that the question is unsettleable given either the current state of human knowledge or the inherent limits of human knowledge. The agnostic atheist responds to this perceived inability to adjudicate the issue by defaulting to non-belief, often out of a principle that it is wrong to believe without sufficient evidence. The agnostic theist, by contrast, opts to believe by faith despite admitting to a lack of sufficient reasons to warrant belief.
The last kind of broad category of atheist might be “someone who lives without gods”. This is often a confusing usage of the word, but it is one in circulation. All too often one will hear a Christian give a testimony about how they “used to be an atheist” when they really weren’t. They weren’t atheists in the truest, most normative senses of “not believers that God existed”. They reveal that they actually believed in God but just hated him or were angry with him or simply didn’t care about him. The angry/hating ones are best called “misotheists” rather than atheists in the standard senses of “not believing in God” that I laid out above. The apathetic ones were just nominal believers. (Were they apathetic while actually not believing in God or caring to investigate the issue, we’d call them apatheists.)
Essentially, monotheism and polytheism are generally so deeply connected with people not just believing in a God or gods but in their supplicating, worshipping, or appeasing a God or gods, that opting out of the entire practice of engaging with the gods is so non-standard to theisms that it could count as a form of effective atheism. Essentially, believing in gods in tangible terms is meant to entail certain behaviors such that if those are lacking, one may as well in practice be atheists. This may partially explain why some people who always essentially had an abstract belief in God may somewhat confusingly say that they used to be “atheists”.
This irks a lot of us atheists because they will present their conversions as proof that an atheist could have the existence of God proven to them when really their turn to becoming behaviorally religious was not at all a matter of acquiring a belief in God by having intellectual atheism refuted. This matters to those of us who know the reasons that intellectually support atheism and are bewildered how anyone who really understood them could flip to affirming all the absurdities required to believe in robustly supernaturalistic forms of theism. It’s true, some smart people do make such an intellectual journey. But they seem to be rarer cases of “atheist to theist” conversions. It seems to be more often that someone does believe and is either apathetic or angry towards God and so doesn’t worship God and calls that “atheism” because it’s a kind of behavioral atheism.
On the flip side, atheists will often count highly secularized people who live effectively like atheists despite nominal theistic affiliations (think Scandinavians) as essentially atheistic. So, while we’re not happy with the merely nominal theist who decides to take their theism more seriously pretending that this involved an intellectual realization that “atheism” was false when they never were intellectual atheists in the first place, on the flip side we (or at least I) are generally happy taking highly secularized Scandinavian societies where theism is almost entirely nominal as model atheistic societies to a significant extent.
So, while it’s confusing when people conflate atheisms that are ontological or epistemological in character (i.e., those which make claims either that there likely is no God or that rational duty demands lacking belief in God, etc.) with “living without gods” atheisms whereby one lives as though gods were irrelevant (whether they’re believed in or not), there is some value in paying attention to the latter usage of the word. Deists and highly secularized people who live and think like de facto atheists often really do reject the behavioral aspects of traditional theisms–the supplicating, worshipping, and intellectually/morally deferring to gods–that are really the most objectionable part of theism and integral to its fully religious forms. So there’s some rhetorical value to us in capitalizing on the connotations of the word “atheism” such that it incorporates those who live as though gods are irrelevant. There’s value in pointing out that the numbers of effective atheists are higher than the stats about self-identifying atheists would let on.
A final key thought here. A lot of philosophers and psychologists argue, with good reason, that to one extent or another beliefs are not simply mental affirmations but have a component of behavioral disposition. (Some go all the way to the point of denying the mental affirmations as relevant at all in ascertaining beliefs–but I don’t.)
It’s one thing to say that I think something is true. It’s another to put my money where my mouth is and act like it’s true. Often there is great cognitive dissonance in the minds of theists who claim to believe there exists a God who severely punishes disobedience while they go on consciously disobeying. Some would argue their behavior reveals either their true beliefs or, at least, the ambivalence of their beliefs. In other words, they may not be strictly theists or atheists but rather adopt theist beliefs and have theist dispositions in some compartmentalized areas of their lives and have atheistic mindsets and dispositions in others. There is also some experimental evidence of atheists having subconscious reactions more consistent with theistic beliefs than atheistic ones too. Belief is a complicated issue, one that goes well beyond just what people explicitly affirm or deny. It may well be that we’re self-deceived if we think of all believing in either/or terms as though people completely believe or completely don’t believe in a great number of cases where people’s behavior would indicate serious fluctuations over time or across circumstances. I delved into many of these issues in some depth in my post, What Does It Really Mean To Believe, Disbelieve, or Lack Belief?
At minimum, the cognitive dissonance, even if it does not signal insincerity of belief, is an opening to challenge someone to live more consistently according to their putative beliefs and putative allegiance to what they say they think about the Bible or the Church or God, etc. The impracticability of this may make clearer the high stakes of consistently living by what they say they believe in and may discourage such cavalier, cost-free, belief statements as they’re accustomed to making (subconsciously as identity markers or status indicators or ways of saying they’re a “good person”, etc.). Emphasizing their cognitive dissonance might also lead to values decisions where they realize that if they had to choose between affirming explicit atheistic beliefs and values that are at odds with their religion but more in line with how they actually live, on the one hand, or having to start living consistently according to the religious beliefs and values they say they believe in now, that they’d be better suited to resolve the cognitive dissonance by being full fledged atheists rather than making many of the irrational sacrifices that being more consistently religious would require. At the least it might at least help them liberalize their explicit interpretation of their religion to show them that they’re not living as though they really believe their more conservative beliefs are true.