At its simplest theism can be defined as the belief in the existence of at least one god, and atheism as the absence of belief in the existence of any gods. The word comes from the Greek, the prefix a- meaning ‘without’ and theos meaning ‘god’.
An atheist’s absence of belief may come from a deliberate choice not to believe, or from an inherent inability to believe religious or spiritual doctrine as literally credible. Atheists are not ‘in denial’ and are not wilfully ignoring evidence of gods. It is possible that someone may be atheist by default, having never been exposed to the concept of gods, but I’ve never encountered this outside of speculation alone.
In discussing the absence of a belief in god or gods the definition of what is meant by ‘god’ or ‘gods’ cannot be immediately assumed, as belief systems vary greatly in various religions, philosophies, and personal beliefs. Therefore, before ruffling any feathers, it might be a good idea to discuss what might be implied, as each response is going to be different with each person involved.
Beyond the Judeo-Christian understanding of gods for example, it may be argued that gods exist in a metaphorical sense. For example, that gods dwell within each individual in the mind, in the conscience, or in consciousness itself. An atheist will not likely dispute that gods can exist metaphorically in an individual’s mind; the disagreement lies in whether or not these gods can exist or not independently of the mind and outside of human belief.
Another form of theism, called animism, describes natural objects such as stones, trees, rivers or even the universe itself as being spiritual beings, even gods. Atheists don’t deny their existence as physical objects, but rather dispute whether or not such objects can be rightly classified as ‘gods’.
The absence of a thing cannot be proven by definition, therefore demanding an atheist prove the non-existence of gods is self defeating (so please don’t do it, it’s very dumb). The burden of proof here lies with the theist. If the theist cannot demonstrate that their belief is reasonable and justified, then atheism immediately seems a perfectly reasonable and creditable stance.
Mere disbelief in the truth of a proposition (in this case, the disbelief in the existence of gods) cannot be treated as equivalent to the belief that the proposition is false and that the opposite is true; neither the world nor most individual belief systems work in such strict duality. If one makes a claim and another disbelieves it, it is not necessarily the same as saying that the claim is false. It may be that the preposition was not understood well enough to determine one way or another, or one may lack the means or information to test a claim, or one may simply not care enough to think about it either way. Atheism may be a chosen by default from lack of knowledge, or it can be well reasoned doubt, or otherwise.
There is a purveying assumption that atheism is a non-religious religion, or an anti-religion, when this simply isn’t the case. If we take ‘religion’ to mean ‘a set of beliefs, values and practices, or a cause principle or activity pursued with contentious devotion’ even omitting reference to gods or a ‘higher power’, atheism still does not qualify as a religion.
Atheists vary greatly in their beliefs and attitudes and it the misconception that atheism means more than what it does is common, and very false. Using our above simplistic definition, atheism is the absence of belief of the existence of any gods. There are no unified beliefs among atheists tying them all together beyond the fact that no atheist believes in a god or gods. No further beliefs about politics, philosophy, society, social conditions, science, religion, etc. are implied. When you know someone is an atheist, all you know is that they do not profess belief in any gods.
Essentially, the difference between atheism and theism has no implicit moral or intellectual significance. The difference lies in the methodological difference between the application of skepticism, reason, and observable physical reality (science) and fantasy, intuition, and tradition in theological matters.