Not sure if there's a formal definition, but this page distinguishes between a scare and a hoax: "Though city prosecutors eventually concluded there was no ill

Not sure if there's a formal definition, but this page distinguishes between a scare and a hoax: "Though city prosecutors eventually concluded there was no ill intent involved in the placing of the ads, the city continues to refer to the event as a "bomb hoax" rather than a "scare." - https://en.wikipedia.org/wiki/2007_Boston_bomb_scare https://en.wikipedia.org/wiki/2007_Boston_bomb_scare