Can you provide links to those definitions, or cite the sources? They both refer to the narrower definition, within the broader one.
See, for instance:
http://en.wikipedia.org/wiki/Atheism
To me, there is little difference between a disbelief and an absence of belief. (To simplify) If something passes a threshold for credibility, it is believable; else it is not. It's the same test I apply to all things in life, whether it be the purchase of a bridge across the East River from Manhattan, or the role of omnipotent magical beings.
Negation of a belief, is not a belief in a negation. Moreover, you are confusing the prefix '
a-' with the prefix '
anti-.
See, for instance:
http://www.wordinfo.info/words/index/info/view_unit/2838/
If I am without a belief in a god, then that's all one can say about that.
EDIT: I see now that some of this has been covered in posts above.