archduchy vs demesne

archduchy and demesne both are nouns.

Word	Noun	Adjective	Verb	Adverb
archduchy	Yes	No	No	No
demesne	Yes	No	No	No

As nouns, demesne is a hypernym of archduchy; that is, demesne is a word with a broader meaning than archduchy:

Other hypernyms of archduchy include domain, land.

archduchy (noun)	demesne (noun)
the domain controlled by an archduke or archduchess	territory over which rule or control is exercised
	extensive landed property (especially in the country) retained by the owner for his own use