Dog and sweet Jebus! I get tired of this question and all variations on it.
Look in all the dictionaries you can find as often as you like, but remember that even though lexicographers try really hard to provide definitions that accurately describe what most English-speaking users mean when they use a word, the lexicographers are mostly Christians, Jews or other monotheists. Hence the use of the capitalized "God" in the definition. Most dictionaries also offer a definition of "God" with a capital g.
There is no practical or operational distinction between saying that an atheist "lacks a belief in gods" or "believes that no gods exist" or "is convinced that no gods exist" or "denies the existence of gods." The difference is merely word choice or semantics. What's the same is how the atheist gets to the mental stance or perspective (of having a conviction that no gods exist, or believing that they don't, or lacking a belief that gods do exist, etc.): Looking for and evaluating the evidence pro or con, and finding that there is no credible evidence supporting the existence of supernatural beings as anything other than man-made inventions.
I adapted the rest of my answer here from one that I posted LESS THAN A WEEK AGO in response to a question stated as "Definitions of gnosticism/agnosticism and theism/atheism: would these definitions seem agreeable to you?"
Yes, agnostics also "lack a belief" in the existence of gods, but there is more to agnosticism than that. In standard English, "agnostic" is never used except to describe a mental or philosophical stance that the existence or non-existence of gods is unknowable or a nonsensical or unresolvable problem.
Both atheists and theists can differ in the level of confidence they express about their belief or non-belief. But quite a few atheists whom I know don't say that they are "99.5 percent certain" or "99.9 percent certain" of their non-belief in gods. They prefer to say that the existence of a personal god (of the sort depicted in the Bible) is so improbable (0.5 percent or 0.1 percent, etc.) that they have concluded no gods exist and choose to conduct their lives accordingly. Agnostics usually conduct their lives in much the same way, according to the same secular, naturalistic worldview. The only difference is that if you ask an agnostic, "Do gods exist?", the agnostic will usually answer "No one knows" or "No one can know" or "That question makes no sense / is unresolvable" instead of "I am 90 percent confident that gods don't exist" -- even if the last statement is a completely accurate summary of the agnostic's "belief" or mental state on the question.
From the New Oxford American Dictionary, 2nd edition (2005):
atheism (n..). The theory or belief that God does not exist. Late 16th cent. from French athéisme, from Greek atheos, from a- 'without' + theos 'god.' -- atheist n. / -- atheistic adj.
agnostic (n.). A person who believes that nothing is known or can be known of the existence or nature of God or of anything beyond material phenomena; a person who claims neither faith nor disbelief in God.
God (n.) 1. [capitalized and without a definite article] (In Christianity and other monotheistic religions) the creator and ruler of the universe and source of all moral authority; the supreme being. 2. god [uncapitalized] (in certain other religions) a superhuman being or spirit worshipped as having power over nature or human fortunes; a deity.
There are no "sects" within atheism, because atheism is not a religion and there is no operational or practical difference between your A and your B.