Rex vs monarch

Rex and monarch both are nouns.

Word	Noun	Adjective	Verb	Adverb
Rex	Yes	No	No	No
monarch	Yes	No	No	No

As nouns, monarch is a hypernym of Rex; that is, monarch is a word with a broader meaning than Rex:

Other hypernyms of Rex include adult male, man, crowned head, sovereign.

Rex (noun)	monarch (noun)
a male sovereign; ruler of a kingdom	large migratory American butterfly having deep orange wings with black and white markings; the larvae feed on milkweed
	a nation's ruler or head of state usually by hereditary right