It seems to me that you are trying to be objective, refusing to take into consideration what atheists, agnostics and theists themselves say about their belief, disbelief, lack of belief. VitalOne seems to be doing just the same. I think an attempt at such objectivism, an attempt to take the issues in question out of their particular contexts, must inevitably lead to explanations that might seem adequate to you, but are inadequate in the eyes of atheists, agnostics and theists respectively. What each of them implies by "belief" is worked out in their particular philosophies - and they differ from one another. I say they are mutually exclusive, so they are separate options. I differentiate between the intention and the externally observable result. If the externally observable result is that I don't accept something, this does not necessarily imply that my intention was to reject it. For example, I don't own any Reebok running shoes, I have only Nike's and Adidas'. This is externally observable. But it doesn't imply anything about how this situation came to be, what intentions brought it about. I do not hold it is adequate to make conclusions about intentions on the grounds of externally observable results.