I don't think it's right to say there are competing definitions, as if they're both equally right. I think there's a correct definition a) "set for life" and a wrong one b) "set for now". These are two very different concepts, so using the same term is causing confusion.
Someone in this thread said "I have FU money for a year", which makes absolutely no sense. This shows how misusing the term can cause confusion.
If you live (relatively speaking) from hand to mouth, and you walk into a negotiation for a small amount of work, it doesn't take much money to be able to say No and mean it; enough money to last a week may be FU money.
It might make sense after all, I can think of several situations in which that is perfectly valid.
For instance, if you have only a year left to live (an extraordinary amount of people die every year, fully 1.6% of those alive today will not be alive next year).
The younger you are the more money you'll need to last you 'forever' (or at least, until that guy with the hoodie and the scythe shows up). I'm 45 so if you're considerably younger than I am you'll probably need more of it. But having 'FU' money for a decade in your prime and then having to go back to work when you're say 55 is probably a lot better than the reverse, retiring at 65 when you're older and physically less capable seems like the wrong way around to me. Get some mileage out of your life while you can enjoy it to the fullest.