There is a variety of ways to handle Fudge points and character development and whether there is a relationship between the two, and I think I have settled on a perfect balance for my own games. First, they are separate. They do not influence one another in any fashion. Second, I minimize the bookkeeping. Any meta-rule I can live without is happily jettisoned.
Fudge points are handled, for the most part, in the standard manner. They are first acquired at character creation and then awarded at the end of a session, but I may also award them during the session if circumstances are appropriate (such as the accomplishment of a particularly daring deed). They may be spent or saved at the player's discretion.
For character development, I opt for the subjective method, which requires no tracking of experience points. Additionally, I allow development through training.
Why am I writing about this? Because I know there is a temptation to create a tension between Fudge points and experience, to make them one and the same or to allow players to spend one in order to purchase the other, but I think it overcomplicates the game and blurs the distinctions in an unhelpful way. Fudge points at their best are a fun way to use a resource to pull off impossible feats or narrow escapes. Subjective character development is an organic way to improve a character without resorting to out-of-character considerations. I can perceive no good reason to link them. And that is how I have decided to handle it henceforth.
