Well, they are about the same.Intimidate implies that you interiorize someone a little. It may not even have been intentional. It could just be that the person who is intimidated is just not able to comfortably face up to something. For example, a sports team from the country comes to the big city to play a team of faster, bigger opponents in a noisy stadium. They may be intimidated even though the other team is not trying to make them so. Menace and threaten are similar. In both cases there is an actual intention to scare or threaten the other party. Menace implies a physical presence. Threaten could also be a physical presence, but may also done by long-distance communication.