You can be atheist agnostic - you don’t actively participate in religion or worship but believe it is fundamentally unknowable if there is or is not a god, you can also be theistic agnostic (though this is rare in the modern lexicon) which would be where you do participate in religion (or religious practices) but still believe it to be unanswerable. To be gnostic is to believe it is knowable (and perhaps that one does know), it too can be either theist or atheist in nature.
Atheism and Agonistism are under the umbrella of Irreligion or Non-Religious. They are seperate identies.
You can be atheist agnostic - you don’t actively participate in religion or worship but believe it is fundamentally unknowable if there is or is not a god, you can also be theistic agnostic (though this is rare in the modern lexicon) which would be where you do participate in religion (or religious practices) but still believe it to be unanswerable. To be gnostic is to believe it is knowable (and perhaps that one does know), it too can be either theist or atheist in nature.