composure vs serenity

composure and serenity both are nouns.

Word	Noun	Adjective	Verb	Adverb
composure	Yes	No	No	No
serenity	Yes	No	No	No

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

Other hyponyms of composure include aplomb, assuredness, cool, poise, sang-froid, placidity, quiet, repose, tranquility, tranquillity.

composure (noun)	serenity (noun)
steadiness of mind under stress	a disposition free from stress or emotion
	the absence of mental stress or anxiety