Is there a word to describe a state of not identifying with any common explanation of God?

I am trying to describe one who is neither agnostic nor atheist but does not accept any religious order as his own.

A theist is someone who believes in god (or multiple gods), in contrast to an atheist.

If you refer to someone as a theist, it will generally be understood that s/he doesn't belong to a specific religious group.

If you really want to emphasize that fact, though, you might say unaffiliated theist. Personally, I don't think the latter is necessary.

An ignostic refuses to take any stance in the argument over God’s or any deity's existence.

The reasoning behind this is that the lack of a sufficiently coherent definition for the term God leaves the question regarding God's existence without meaning. Thus, the ignostic would argue that there is no basis for sensible discussion on this topic, let alone basis for belief or non-belief.

Someone who believes in God is a theist; all Christians, Muslims, Hindus (but not Buddhists, since Buddhism does not have a god), etc. are theists, as are people who don't subscribe to any major religion but still believe in God.

A subset of theism is deism: Someone who believes in a creator-God that does not get involved in our personal lives believes in deism and is a deist, and is in the company of Albert Einstein, Benjamin Franklin, and Voltaire.

There is no single term that I know of to describe someone that doesn't follow the tenets of a major religion but does believe in a God that impacts our lives, which is odd because (I believe) this is a reasonably common belief in the US. An old phrase used to describe this belief, though, is "I'm spiritual but not religious.", which implies that you have faith but not in an organized religion.