demesne vs imperium

demesne and imperium both are nouns.

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

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

demesne: territory over which rule or control is exercised
imperium: the domain ruled by an emperor or empress; the region over which imperial dominion is exercised

demesne (noun)	imperium (noun)
territory over which rule or control is exercised	supreme authority; absolute dominion
extensive landed property (especially in the country) retained by the owner for his own use	the domain ruled by an emperor or empress; the region over which imperial dominion is exercised