In Monsters University, the artists had to alter their designs in order to make the prequel setting believable. It was set in the 80's, whereas Monsters Inc took place in the 90's, so it was interesting to see the subtle changes between films.
The character designs didn't change too much between the films, but "a hook" was added to the university students to make it obvious that it was the same monster but younger, such as Mike's retainer, and Sully's hairstyle/size.
Randal has an interesting character development, because at university he is wearing glasses which portray his originally nerdy personality, which kept the audience curious as to how he changed from a good student to the evil character in Monsters Inc.
Another way to keep it relatable to the audiences was to re create the stereotypical feel of the American university lifestyle with sororities and traditional campus grounds, but adapting everything to how the artists envisioned the monstrous world.
The background characters add to the atmosphere of the film; the designers created a few main types of monster to feature, then adapted each design to look slightly different, using a certain colour scheme and having a body structure for reference.
Every aspect of a film is important to telling a narrative, especially a prequel/sequel because the audience already has an idea of how it could look.