peace of mind vs tranquillity

peace of mind and tranquillity both are nouns.

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

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

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

peace of mind (noun)	tranquillity (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