Sri Aurobindo has used both words. His earlier writings has the word God much more often. The reason why he has used the word Divine later on and much more frequently is because the word God has been corrupted by all kinds of meanings, especially Semitic ideas, into this word. The word has been distorted so much by certain human conceptions of God as a judge busy punishing and rewarding human beings based on whether they praise him or not, that it instantly evokes certain negative reactions in the younger generation or an image of a bearded old man sitting outside creation far away from His creatures and the world He has built. The word Divine, on the other hand is used as a noun, adjective, even as a qualified verb implying a more comprehensive sense of all that is high and good and true and beautiful as well as all-comprehensive and an omnipresent reality. It implies at once Being and the Becoming whereas God generally refers to a Being usually outside and above the creation.
Of course the problem is only in the English language. In Hindi or Sanskrit the meanings are precise, each representing something of that ultimate Reality. Thus the equivalent of God as Ishwara implying the Lord (over His creation) and Bhagawan ( full of delight) or Brahman (Vast) are much more accurate. It is the limitation of the English language that proper terms for the highest Reality feels inadequate.
Affectionately,
Alok Da
