calm vs tranquillity

calm and tranquillity both are nouns.

Word	Noun	Adjective	Verb	Adverb
calm	Yes	Yes	Yes	No
tranquillity	Yes	No	No	No

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

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

calm (noun)	tranquillity (noun)
steadiness of mind under stress	a disposition free from stress or emotion
wind moving at less than 1 knot; 0 on the Beaufort scale	a state of peace and quiet
	an untroubled state; free from disturbances

calm (adjective)	tranquillity (adjective)
(of weather) free from storm or wind
not agitated; without losing self-possession

calm (verb)	tranquillity (verb)
cause to be calm or quiet as by administering a sedative to
make steady
make calm or still
become quiet or calm, especially after a state of agitation