I believe these are both correct.. If you want to say that a warning or signal (that was sent by someone, etc) and it turns out there really wasn't a bomb after all, this would be correct. A bomb threat, would be a danger. a threat = an immediate danger to happen by something. (basically) and if there isn't danger after all, then it too, can be false. But technically, these sentences don't mean the EXACT same thing, of course. But the idea is the same. The way you put the sentences together are OKAY though :)