Yes, we've slipped back to C after only a brief foray into D-land. Sorry.
Character-led fiction is those series of stories that are initiated by the publisher and often written by a whole team of writers. The first famous one was probably Animal Ark, written not by Lucy Daniels but by a collection of writers-for-hire. Publishers like character-led fiction because they don't have to pay very much for it and these series usually sell lots of copies.
The degree of control you are given over the story varies between publishers and lists. You may be supplied with a title, a set of characters, a plot outline and a 'bible' that will cover all the details that need to stay the same between volumes, such as the name of the protagonist's dog, their parents' jobs and do on. It really is like painting by number but with words. At the other end of the scale, you might just be given a title and the characters. Although this gives you more freedom, there is also a much greater chance of the editor coming back with niggles such as 'your plot is too similar to writer x's plot' or 'oh dear, the dog is called Slug in the other book...' (Problems which could have been avoided by having a bible.)
You won't have your name on any character-led fiction you write, which is probably a good thing as it tends to be anodyne and unchallenging. If you're given a full plot, it's not very interesting to write. But it can be a useful way of giving yourself a bit of training (at least in obedience) and gives you the chance to write in a style you might otherwise never try .
The pay varies. You might get a small royalty, or you might get a flat fee. You should try to make sure you get the PLR. If you can knock them off quickly and don't mind feeling like a writing slut, they're quite a useful source of income. It's not high art, but you can get some satisfaction from writing within strict boundaries and it can hone your plotting and character development skills. It's the equivalent of practising your scales, really. If you want to give it a go, Working Partners is a good place to start.
Before you attack my snobbish attitude, I'll just point out that I have actually done it and I am absolutely a writing slut - I'll write almost anything if someone is going to pay me.