One way the Atheist/Agnostic division is conceptually understood is as a question of epistemic strength regarding a suggested proposition that "Nothing exists that might be appropriately called a god or God". An Atheist thinks there is sufficient reason to believe such a proposition - an Agnostic thinks that there is not. (Both would in agreement that there is not good reason to support the contrapositive)
(There is sometimes a distinction drawn between Strong Atheism, which affirms that no Gods exist at all, and Weak Atheism, which affirms that nothing that they believe in is a God. This is a question about the scope of the existence claim - both Strong and Weak Atheists ought to agree to the statement, but Strong Atheism simply asserts that this is the case of a Final, True Metaphysics, which a Weak Atheist need not, being content to talk about their own ontology.)
One common Atheist position is, as you say, to cite the consistent failure of religious traditions as supporting evidence of an inference to the best explanation. This is, practically, quite a useful piece of abductive reasoning, in that if there is no good practical reason to support any positive claim to God's existence then one might as well assume that it does not and save one's self the cognitive or emotional labour involved in trying to leave room for it.
However, there are also good practical reasons for a position of suspending that belief. Some positions regarding theological discourse are Anti-Realist, which is to say that "God" is primarily a matter of a language which comes apart from a straightforward reading of concrete facts. The suggestion is not that "God does not exist" is true or false, but rather that neither "God does exist" nor "God does not exist" are wholly transparently apt to being true or false. I might hold, for example, that there are alternative translations of what Theists are talking about that makes some of their utterances about God true or false in select ways, and others that might just not make sense.
The Atheist position (in either Strong or Weak form) is a realist one, in that they accept that truth-conditional sense is made of what it means to be a god or God, but reject that there are any. The belief to the effect that no gods or Gods exist commits us to an interpretation of what "gods or Gods" might be. As such, this technology of anti-realist interpretation is harder for them to justify.
Agnostics are not obliged to settle on a theology in order to ground their absence of beliefs in reason, where Atheists must have some settled interpretation of what truth conditions ground their use of language in affirming that God does not exist. This flexibility of interpretation is of further practical value when engaging with others who do have theological beliefs that inform their behaviour, or when dealing with a plurality of possible traditions of theological beliefs.