But how does one define "god?"
God has a will. With the exception of certain Deists, who I understand to think of God as little more than an explanation to existence itself, all other Theists believe that there is a higher plan or purpose, while Atheists do not.
However, I am confused. Your thread title compares Theism with Atheism, while the OP text seems to be more interested into distinguishing Theism from Religion, or Religion from Spiritualism.
Personally, I do not distinguish Religion from Spiritualism at all, although it is true that in certain contexts there is an implication that "Religion" is supposedly external in some significant sense, while Spiritualism is perhaps self-ruled. That is not a distinction that I like to use, though.
As for the link between Theism and Religion, I don't think it is much more than a prejudice. The two things are pretty much unrelated, and I would even say that Theism is a bit detrimental to Religion in a general sense.