While not a difference in the world-building or setting of the well-established Equestria, the writing of the manga is considerably different than the comics and show. The manga is much more prone to use gags, slapstick humor and the emotions characters are meant with are typically greatly exaggerated. Personalities and characterizations in general are much larger and much more exaggerated, an example would be Twilight crying and wallowing in self-pity after she didn't lift her hooves at the proper time ("Super Serious Twilight").
Due to the short natures of the stories, there is a noticeable lack of multiple characteristics that define the main continuity, such as: Adventures of large and small scales, mythology and consistent continuity. Instead, the manga offers light-hearted, humorous short stories that contradict one another.
While the character designs are largely unchanged, there are slight differences. Twilight's fur is considerably lighter in some shots, to the point where it borders on a pink coloration instead. However the biggest change would be the expressions and injuries the characters take or suffer. As typical with anime, characters tend to go "off model" several times to heighten the comedic value, and injuries such as bumps or bruises are greatly exaggerated.