A word that can be used in multiple ways is said to be "polysemous" or to have a "polysemous characteristic."  For example, while the word "colour" is most commonly used in describing the visual appearances of objects, environments, etc., it's also polysemous because it can be used in other ways, such as metaphorically to describe a person's character (e.g., events in their past have taken on a different colour), to describe bias (e.g., the racist is not colour-blind), to indicate a factor of influence (e.g., the presenter coloured the audience's perceptions), etc.

In the case of atheism, the known variations, which also include a broad range of positions, all entail the classification of the "absence of belief in deities," which fundamentally characterizes atheism (and atheists) who prefer to include specific positions.  Some common variants we've encountered are:

atheism - absence of belief in deities
(included here for completeness)

This is the purely fundamental classification of atheism that is consistent with etymology/history, linguistic structure, logical usage, and common understanding.  Some alternatives include:

• apostates (post-theism and intended as derogatory)
• baby-eaters (false derogatory slang that implies cannibalism)
• brights (false derogatory slang that implies higher intelligence)
• heathens (false derogatory slang that implies polytheism)
• non-believers (limited usefulness, such as in conversations about theism)
• non-conformists (a general category which atheists are included in from the perspective of theists who arbitrarily expect theological conformity)
• non-theists (synonym of atheism that's uncommon, possibly due to being more awkward-or-cumbersome to express than "atheism" in both verbal and written forms)
• nones (informal slang that is commonly confused with Nuns from Catholicism due to their homophonic characteristic)

This entry ("atheism - absence of belief in deities") is always correct since it has the broadest scope and is polysemously shared by all variants.  When the words "atheism" and "atheist" are not clarified in any written works (incuding academic texts and philosophical papers), this is the standard definition that is naturally presumed as "normative" by the majority of readers.

antitheism - the position or belief that deities do not exist

This is an anti-theistic position, which is somewhat regularly hyphenated as anti-theism, that commonly also consequently includes the "absence of belief in deities."  Historically, some dictionaries did unfortunately cite only this definition for their "atheism" entry, but such instances have gradually become less common as most publishers have been correcting and updating their definitions accordingly (e.g., Merriam-Webster updated their definition of "atheism"³⁷ on January 30, 2019, and "atheist"³⁸ on December 5, 2018).

The logical problem with this variant is that it incorrectly attempts to limit the scope of the meaning that leads to attempts to incorrectly impose an onus of justification (a.k.a., a burden of proof) onto atheists who don't actually hold such a position.  One of the reasons some theists continue to use this manipulative tactic is that when debating an adversary who does not hold an opposite position, they feel disadvantaged due to their own lack of confidence and conviction about their own position, which contrasts with an adversary who does hold the opposite position and can therefore serve as a convenient diversion.

dogmatic atheism - the doctrine that there is no god

This is an anti-theistic position that also consequently includes the "absence of belief in deities," but it's most commonly known as a defective dictionary definition that fails because atheism doesn't have any doctrine, religious or otherwise.  Doctrines are generally important pinnacles of religions that are usually refrred to as scripture and/or holy books.

The factual problem with this variant is that it never includes any actual references to the very doctrine it falsely claims atheism is comprised of.

lacktheism - the lack of belief in deities

When this variant is used, the word "lack" is usually meant as a synonym of the word "absence."  However, the introduction of the derogatory neologism "lacktheist" is that it often implies an intention of intellectual dishonesty by attempting to draw attention away from the impartial nature of the classification of "absence of belief in deities" in favour of creating a bias of non-objectivity among atheists.

The problem with this variant is that it incorrectly implies that atheists are abnormal due to being bereft of belief in one or more deities, and attempts to categorically stigmatize atheists - incorrectly and in a bigoted fashion - as intellectualy dishonest.

misotheism - the hatred of god

The miso- prefix is a hostile emotional characteristic that is incidental to atheism, but which does include atheists who feel hatred toward deities along with any theists who hate deities from competing religions or, in some instances, even their own religion.  Although it's not uncommon for some theists to incorrectly conclude that non-believers hate the deity/deities they feel love and admiration for, hatred and other emotions are incidental to atheism because they're simply not addressed by the definition of the word "atheism."

Calling someone a "god-hater" also normally qualifies as derogatory slang because it relies on a bifurcation fallacy (a specific type of false dilemma) that is typically found in religious scripture (e.g., Matthew 12:30 in the King James edition of the Holy Bible states "He that is not with me is against me; ...").

The logical problem with this variant is that it incorrectly attempts to vilify atheists without regard for the neutrality of not believing in deities, which is categorically incidental to an atheist's emotional or otherwise psychological state.  One of the reasons some theists continue to use this manipulative tactic is that it's often easier to sway an audience to disfavour an adversary who is perceived to be biased for having hateful emotions.

neoatheism - ferociously anti-religious

The neo- prefix indicates something that's "new" or "recently revived."  Combined with "atheism" it became well-known with a negative connotation as a social anti-religious movement that promotes a ferocious antagonism against religion that erupted in the early 2000s.

The problem with this variant is that it incorrectly depicts atheists as being extremely hostile toward religion.

Further reading

• Dictionary definitions and other helpful references
• Quotes of interesting perspectives from interesting people