A Duke is the head of a Duchy with a Grand Duke being the head of a Grand Duchy. Generally the highest rank granted to a land holder in a Kingdom; can be independent and autonomous as a Duchy without being directly vassalized to a Kingdom.
In the Republic
Within the Republic, the title of Duke is given to the sovereign when organized as a feudal Crowned Republic. It is used mostly to signify the rank and tier at which the Silver Sun operates in relation to other organizations. The Republic does not operate as a full Kingdom, but more as a city-state a la Florence or Venice in a historical sense.