earldom vs demesne

earldom and demesne both are nouns.

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

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

Other hypernyms of earldom include domain, land.

earldom (noun)	demesne (noun)
the domain controlled by an earl or count or countess	territory over which rule or control is exercised
the dignity or rank or position of an earl or countess	extensive landed property (especially in the country) retained by the owner for his own use