Mushroom World is the name of the planet Mario and his friends reside on. The Mushroom World is the greater setting of most of the games in the Mario series and sub-series.
The Mushroom Kingdom has various other lands and kingdoms associated with it, such as Yoshi's Island, the Beanbean Kingdom, and Nimbus Land, and many other locations, also from the Donkey Kong series, all exist on the Mushroom World. Outside of Super Mario Bros. Z, other video game characters will come to the area, such as the Mario, Sonic, Donkey Kong and The Legend Of Zelda series' (only Link).
Super Mario Bros. ZEdit
In Super Mario Bros. Z, the Mushroom World has been in grave danger since Mecha Sonic's and Dr. Eggman's appearances, as well the Chaos Emeralds. Sonic and Shadow have appeared to the Mushroom World from their home world, Mobius.