Theism and atheism refer to a belief or lack of belief in the existence of god(s).
Gnosticism and agnosticism refer to a (claim of) knowledge of the existence of god(s).
I'd consider myself an atheist because I don't personally believe there are gods, but I'm also agnostic regarding the possibility.
I don't have enough info to rule out the possibility of a deity or deities, but I don't have any reason to believe there are any (or at the very least, not any that have a direct and personal interaction with humanity).
Belief = assumption + ego. I prefer to use the word assumption, it’s much cleaner and means the same thing as belief, without invoking emotions.
Therefore I don’t see any difference in assuming or not assuming the existence of god(s), and knowledge of the existence of god(s), which are still assumptions anyway.
I’m only seeing the utility of defining the following 3 groups:
1) assumes existence of god(s)
2) assumes lack of existence of god(s)
3) assumes nothing regarding the existence of god(s)
“I do not assume that there is a person in Argentina called Smergold Abrahamson, as that is a ridiculous name. But I am not going to claim with certainty that they do not exist”.
Which is more concisely re-written as:
“I assume there is a very low probability of the existence of a person in Argentina called Smergold Abrahamson”.
Which going back to the original comment, I see the difference now:
“not believing (assuming) in a higher power”
is different than
“claiming (assuming) no higher power exists”
Although, I guess my personal definition has been that theist assumes a higher being exists, an atheist assumes no higher being exists, and agnostic assumes nothing.