Both words refer to someone or something that poses a danger to us. A threat in this sense is not the verbal warning (Is that a threat?), but something that jeopardizes, or could jeopardize, life, peace, health, or other desirable conditions currently intact: a threat to national security. Menace can be a strong synonym for threat, when the harm is imminent or even already occurring, as with the menace of crime, corruption, pollution, and stray dogs.The difference in meaning can be seen in the verbs that typically precede each word. We want to eliminate a threat before the harm comes to pass, but a menace already has a troubling presence we tackle, curb, deal with, or eradicate. Gang culture is a threat to the community, whereas the presence of gangs has become or is a menace.