Q: What's the difference between a "weak atheist" and a "strong atheist"?
A: A weak atheist is one in whom no god-belief is present. A weak atheist makes no claims about the general existence of a god or gods, he or she simply has no belief in any them.
A strong atheist, on the other hand, not only has no god-belief, but also makes a positive assertion that in fact there are no gods at all.
Weak atheism is an absence of belief. Strong atheism is an active belief.
On this site, the general word "atheist" is generally equivalent to "weak atheist".
For more on this distinction, see Wikipedia.