How does a theocracy differ from a monarchy?

Monarchy is rule by a king, prince, emir, sultan, or other hereditary power-holder. Theocracy is rule by a religious leader or a person who is believed to be a god-in-the-flesh. In many societies, monarchies have been theocracies since the king was believed to be a physical god, such as in ancient Egypt or as recently as World War II Japan. However, you can have monarchies that are either secular states or states where there is an official religion, but this religion does not have ruling power. You can also have theocracies where the rulership comes to power via internal appointment or quasi-democratic election as opposed to heredity, so these would be non-monarchic theocracies.