What is the difference between not believing in a higher power and claiming no higher power exists?

I lack a belief that there is a person in Argentina called Smergold Abrahamson, as that is a ridiculous name and I have no reason to believe that they exist. But I'm not going to claim with certainty that they don't.

I think the word believe is unnecessarily complicating this. As I stated above in another comment, assumption is a better word to use than believe, so substituting that gives:

“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”