Genuine Question? Fatal Fury or King of Fighters?

I hear people often using these names loosely to talk about this series of fighting games I am unsure what it’s true title is because some people refer to this as the Fatal Fury series and others refer to it as the King of Fighters series… but I just don’t get it both names make sense and both names are used to represent the series as a whole… not even Smash Bros is sure whether to call this Fatal Fury or King of Fighters.

What is the true title of this video game series?