To me, God is a very specific word. When it is capitalized like this, it might be defined as a supernatural being that created the Universe, is revered, and holds judgment over the beings He/She has created. If it is not capitalized, then it could be any supernatural being that has some kind of control over something in the material world, like a god of trees, or a god of oceans. These words were used by early civilizations and cultures to explain things that didn't seem to have a logical cause, but could cause great harm or great fortune.
I would give more intellectual leniency to a term like Higher Power. A Higher Power could be God, but it could also be the laws of physics, or simply, Nature.
I think when you use the word God, it implies personification of the unknown to a supernatural being to most people, even if you don't mean it that way.