demesne vs earldom

demesne and earldom both are nouns.

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

As nouns, earldom is a hyponym of demesne; that is, earldom is a word with a more specific, narrower meaning than demesne:

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