1.) That an individual adheres to a given religion and its attendant god or gods.
2.) One holds to no religion and no belief in a god or gods, a state referred to as a-theism.
However, what we see in practice is more often in-between these positions. On the one hand, most except the concept of some form of a god as the probable truth, and delve no deeper than this surface gloss, (most likely due to the fear of ignorance on the issues involved) but assume there are answers "out there" to meet any objections which may arise.
As an atheist, I have no objection to the philosophic contention or contemplation of a god or gods. Rather, it is the un-reflecting acceptance of such a position which troubles me.
As outlined above, most individuals hold to some vague theism, and find renunciation of it, in an absolute form, to be socially unacceptable. It does not often occur to them that they are themselves engaging in a form of weak atheism/theism. The commonly held view that everyone should adhere to some form of theism is not the same as belief in a religion. At the risk of creating a false dichotomy, one may be theistic and non-religious, and one may be religious but non-theistic, but to be theistic and religious implies a deeper commitment which entails sacrifice and adherence to a set of prescribed dogmas, that most, in an increasingly materialistic society, are unwilling to risk preaching lest they be held to their standard and found wanting.
That it is possible to be religious but non-theistic is exemplified by Buddhism, where belief in a god of any kind is not essential. That it is possible to be theistic but non-religious is nobly demonstrated by Spinoza, whose pantheistic god makes worship and prayer in vain, if not solipsistic. Yet, both sides of the coin contain within themselves a structure, or a set of values which serve to guide the initiated. In contrast, the vague quasi theism of many Americans (neither genuine religion nor genuine philosophy) may be viewed as either cowardly or ignorant, or a combination of the two. Cowardice for the lack of a deeper commitment to what should be paramount issues in one's life, courage for greater introspection, and perhaps ignorance of the skills necessary for unbiased self-reflection. Thus, one ends up filling the gap between commitment and conviction, and the conveniences of secular modernity, with a god cut to size. A state even more broad in its interpretation of theology than Cafeteria Christianity, and twice as hollow.