peace of mind vs tranquility

peace of mind and tranquility both are nouns.

Word	Noun	Adjective	Verb	Adverb
peace of mind	Yes	No	No	No
tranquility	Yes	No	No	No

As nouns, tranquility is a hypernym of peace of mind; that is, tranquility is a word with a broader meaning than peace of mind:

Other hypernyms of peace of mind include quietness, quietude, tranquillity.

peace of mind (noun)	tranquility (noun)
the absence of mental stress or anxiety	a disposition free from stress or emotion
	a state of peace and quiet
	an untroubled state; free from disturbances