threat vs menace

threat and menace both are nouns.

Word	Noun	Adjective	Verb	Adverb
threat	Yes	No	No	No
menace	Yes	No	Yes	No

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

threat: declaration of an intention or a determination to inflict harm on another
menace: a threat or the act of threatening

Other hyponyms of threat include commination.

As nouns, threat and menace are synonyms defined as:

threat (noun)	menace (noun)
a warning that something unpleasant is imminent	a threat or the act of threatening
declaration of an intention or a determination to inflict harm on another	something that is a source of danger
a person who inspires fear or dread
something that is a source of danger

threat (verb)	menace (verb)
	act in a threatening manner
	express a threat either by an utterance or a gesture
	pose a threat to; present a danger to