monarch vs Rex

monarch and Rex both are nouns.

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

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

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