Royal dukedoms in the United Kingdom
In the British peerage, a royal duke is a member of the British royal family, entitled to the titular dignity of prince and the style of "His Royal Highness" who holds a dukedom. Dukedoms are the highest titles in the British roll of peerage and the holders of these particular dukedoms are Princes of the Blood Royal. The holders of the dukedoms are royal not the titles themselves. They are titles created and bestowed on legitimate sons and male-line grandsons of the British monarch, usually upon reaching their majority or marriage. The titles can be inherited but cease to be called "royal" once they pass beyond the grandsons of a monarch. As with any peerage, once the title becomes extinct, it may subsequently be recreated by the reigning monarch at any time.
Courtesy titles in the United Kingdom
Titles with the same name as a peer's main title are also not used as courtesy titles. For instance, The Duke of Westminster is also The Marquess of Westminster and The Earl Grosvenor (amongst other titles). The duke's eldest son is not styled "Marquess of Westminster" (which would cause confusion between the son and the father), and so is styled "Earl Grosvenor" instead. The title used does not have to be exactly equivalent to the actual peerage: the eldest son of the current Duke of Wellington is styled Marquess "of" Douro, although the actual peerage possessed by his father is Marquess Douro (not "of" Douro).