>>In search of better words, let's say that they don't believe there is a God, but they also don't deny the possibility. So they never participate actively in discussions about religion. They let the believers believe, and let the "unbelievers" "unbelieve".
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>This is a different. In your first sentence above you wrote " ... they don't believe there is a God.". Hence they are a believer. They dont know if God exists or not yet they chose to believe there is not. Hence they are a believer.

Not necessarily. My take is that there's no way that a god, such as described in the scriptures of major monotheisms, can exist, except the way it does now, as an idea. Furthermore, the whole concept was honed over the millennia to evade logic (slight changes in the translation, large changes in the interpretation of the scriptures), to the point that neither existence nor nonexistence can be proved. Third, the very idea of proving is contrary to the idea of believing, which is a strict requirement if you want to be a member.

BUT - it is not impossible, however improbable, that some kind of entity may exist, which would have a number of divine properties, sufficient to qualify as a god under some definitions thereof. So, the agnostic does not believe the actual deity in case exists as such, but then also can't conclude the nonexistence to an infinite number of decimals - so because of this little probability, doesn't completely exclude it either.

Neither of this would fall under the definition of believing - holding true despite lack of evidence or despite evidence to the contrary.