peace vs treaty

peace and treaty both are nouns.

Word	Noun	Adjective	Verb	Adverb
peace	Yes	No	No	No
treaty	Yes	No	No	No

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

Other hypernyms of peace include accord, pact.

peace (noun)	treaty (noun)
a treaty to cease hostilities	a written agreement between two states or sovereigns
the absence of mental stress or anxiety
the state prevailing during the absence of war
harmonious relations; freedom from disputes
the general security of public places