They're separate things, but they are related, low grip at the front = understeer, not fun. Folks think that if they put an MX5 on cheap tires that it'll be more fun because skids, but in reality, it's better with a little more grip so you can lean on the front end and shift the balance in a predictable manner. The cinq I mentioned was fun at very low speeds, but on a decent bit of road, corner entry speed was very restricted, even under the limit - a Ka or Fiesta would be more fun.
Feedback and weighting have more to do with steering feel, you can have a car that handles great but has numb steering and a car with some handling quirks, but gives great steering feedback. There is the seat of the pants factor of course that comes with a nicely balanced car of course. In a sense, you could define fun handling as the ability to move the grip around front to rear on demand to adjust the cars attitude in a corner.
Feedback and weighting have more to do with steering feel, you can have a car that handles great but has numb steering and a car with some handling quirks, but gives great steering feedback. There is the seat of the pants factor of course that comes with a nicely balanced car of course. In a sense, you could define fun handling as the ability to move the grip around front to rear on demand to adjust the cars attitude in a corner.