I would phrase category A differently: when the work is valuable for its own sake. That's not necessarily fun. It's more likely grueling. Even when it's fun, the fun parts don't add up to nearly as much fun as the painful parts do pain. Yet one can continue because one senses (I almost wrote "knows" - can one know?) that the work is valuable, necessary, important. That's deeper than fun.
What I find interesting is that this comes from within. The other two motivations you list are external. I wonder if the external ones burn out sooner.
When your motivation is intrinsic (that is, you have a felt sense of the work and you know what it is and you think it's important) you have a basis for deciding when to listen or not listen to other people's opinions. But when it's extrinsic, you're more likely to do what other people say and perhaps give up if it doesn't work.
Edit: another thing about intrinsic motivation is that because other people don't have the same sense that you do, what you're doing may seem absurd and they will tell you you're doing it wrong. So the challenge of this path is not just the work is hard and that you fail a lot; it's also that it will probably force you beyond the pale of social proof, something humans are not hard-wired to enjoy.