The territory of duke or duchess is called a Duchy.
A duke (male) or duchess (female) could either be a monarch ruling over a duchy or a member of royalty or nobility.
A duchy refers to a country, territory, fief, or domain ruled by a duke or duchess. The term duchy is employed almost exclusively in Europe, where nowadays there is no sovereign duchy left.
A grand duchy refers to a country or territory whose official head of state or ruler is a monarch bearing the title of grand duke or grand duchess.
