In a shared world setting several authors agree to a world setting, characters, environment and such. The authors then write stories in parallel that occur in this world. The stories may be time-wise distinct, they may follow a common thread, etc. But they frequently each work on their own little story separately. In a cooperative fiction much of the same basis exists.
Several authors agree to a world, setting, characters, environment and the like.
Instead of writing independent stories, though, they write a single story together. Frequently in the cooperative fictions you will find here there is a very strong element of role playing. An author will tend to identify with, design, and write specific characters. Other authors will tend to write the characters they created. Some swapping does occur from time to time depending on the chapter or episode involved but the impetus for how a character acts in a situation is determined by that character's creator.