I think of Deism as the idea that a transcendent God created the universe, and possibly the laws that govern it, then withdraws and takes no further part. It's not that much different from atheism, but seems to be a way of avoiding the difficulty of how the universe came into being if one adopts a physicalist worldview. Theists, however, believe that the creator God is still involved in the affairs of the world and actively intervenes. This seems to me to be different from Pantheism, the most common interpretation of which is, as you say, that the universe is the physical, immanent manifestation of God. The most obvious example of Theism is the Christian idea that God sent his only begotten Son to rescue humans from sin.

(Evolutionary) Panentheism seems to me the best explanation.