Entirely different in scope or description from someone or something that was just being discussed. I'm fine with you going out tonight, but if you want to stay out past curfew, that's another story entirely!
(quite) another ˈstory,
a (quite) different ˈstory
1 very different from what has just been said: Her English is excellent, but her French is another story.
2 used when you are talking about one thing and then mention another thing, which you are not going to talk about on that occasion: I once met Paul McCartney, but that’s another story. I’ll tell you about that one day.