composure vs disposition

composure and disposition both are nouns.

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

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

Other hypernyms of composure include temperament.

composure (noun)	disposition (noun)
steadiness of mind under stress	the act or means of getting rid of something
	your usual mood
	a natural or acquired habit or characteristic tendency in a person or thing
	an attitude of mind especially one that favors one alternative over others