Implicit atheism
No belief in God but no disbelief either. Synonymous to nontheist.

Explicit atheism
Certainty that there is no God.

For simplicity and clarity I use atheist to mean Explicit atheism (there being no synonym for that) and nontheist for Implicit atheism.

There can be both (implicit) atheistic agnosticism (God is unknowable and may or may not exist) and theistic agnosticism (God does exist but we can't know the nature of 'em).