The concept of fighting words comes from a single US Supreme Court case - Chaplinsky v New Hampshire, 315 U.S. 568 (1942).

The short of it is that the circumstances in Chaplinksy were quite unique and in the 77 years since it was decided there has never been another case of a conviction upheld on the basis of fighting words.

Although Chaplinksy has never been explicitly overturned, nobody actually believes that its still valid or that fighting words still exist as a legal concept.

If you're just wondering how the words in Chaplinksy were different from a threat - Chaplinksy didn't threaten anyone. He was arrested for a long, profanity ridden rant that ended with him calling a police officer a fascist.