serenity vs composure

serenity and composure both are nouns.

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

As nouns, composure is a hypernym of serenity; that is, composure is a word with a broader meaning than serenity:

Other hypernyms of serenity include calm, calmness, equanimity.

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