Coming from complete ignorance, I think a deity should have a trait that common mortals don't have and probably can't attain either, like immortality. Deity does sound like a word best used to describe polytheistic religions, at least that's my experience in this corner of the world. Maybe as a society we keep changing the name we have for sacred simbols to avoid hurting the current reigning cult, that might be why deity sounds distant but god sounds close.