"Is atheism the belief that there is no god (or are no gods)?
Or is atheism specific non-belief that there is a god (or gods)?"
I think it's the former. Firstly, if it were to be defined as the latter it would require that the long-standing meaning of atheist be abandoned and secondly the definition you propose excludes millions of Atheists, probably the majority, who very definitely do believe that there is no God. They would have to abandon the label, something I'm pretty sure they would not be prepared to do.
The second definition you gave doesn't quite make sense, IMO. You can't have a "specific non-belief that there is a God or Gods", without an accompanying "non-belief" in the definite absence of God or Gods. Otherwise, the non-belief is really a belief, as exposed by the "non-belief" not being extended to the other possibility. To apply "non-belief" selectively in this way reveals bias and so reveals belief. After all, neither position can be categorically proven, therefore to lean one way or another is to make the same mistake just in a different direction.
To put it simply, if an atheist truly embraced the concept of 'non-belief', they would be agnostic LOL.