I've got to find a better word. "Non-Theist" is assumed by atheists to be the same as their rejection of anything divine while traditional religious types just can't seem to imagine the divine as anything other than an invisible person, granting (or denying) requests, deciding (for some strange reason) when people will die, and sending the occasional natural disaster.
I believe in the Sacred. Mystery. Wonder. Awe. The interconnectedness of all living things. I believe in Intelligence, Wisdom, Love, and the amazing Process of life. I believe in prayer (though I may call it thought, feeling, wishes, visualization, or hope). I refer to my prayers being "received" rather than heard. I sometimes even call the Whole in which I believe, of which I am a part, and in which we all "live and move and have our being," God. I believe in God, I just don't believe in the God I used to believe in or that others seem to accept. My God is more than any image or name or understanding. God symbolizes infinite possibilities, extravagant love, deep wisdom, the unity of all that is. God is a clumsy word for that which can't be named. It's often the best I can come up with, but it's still just a word that represents what can't be known and what can't be limited by human understanding or language.
Emptiness - that's the Buddhist attempt to name what is "really Real."
Inward Light - that's what the Quakers came up with.
Mind - that's what some of the ancient Greek philosophers called It.
Ultimate Reality - I believe that's one of the terms Hindus use.
The Universe, the gods, Spirit...different names, all pointing toward the eternal Truth. Allness. Isness. "God."
Panentheism tells us that God is in us and we are in God. Theism believes in a God outside ourselves. Deism believes in a Theistic God who retired. Pantheism believes that God is in every living thing. But Panentheism believes that God is everything but the Whole is MORE than the sum of Its parts! How can you adequately name that which is All and More? My brand of non-theism is actually panentheism, but that requires explanation, too.
I'll keep working on it, but I dread the day I succeed at finding a term. Because once you can name and explain a thing, you have diminished it. And a diminished, understandable deity is just one more false idol that needs to be destroyed so that the search for the Infinite can resume.