sheikdom vs demesne

sheikdom and demesne both are nouns.

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

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

Other hypernyms of sheikdom include domain, land.

sheikdom (noun)	demesne (noun)
the domain ruled by a sheik	territory over which rule or control is exercised
	extensive landed property (especially in the country) retained by the owner for his own use