Super Taskforce Squad's Adventures in The Super Mario Bros. Movie

Synopsis:

Join Mario, Luigi, Sonic, SpongeBob, and all of their friends as they travel from Brooklyn to the magical Mushroom Kingdom alongside Princess Peach and Toad. But when Bowser, Eggman, and the Villain League plan to conquer every world with the power of the Super Star, it's up to the Super Taskforce Squad and their allies to rise up, race across Rainbow Road, and face an ultimate showdown that will decide the fate of all universes.

Differences:

Mario and Luigi don't get separated in the Warp Pipe-Luigi ends up in the Mushroom Kingdom with Mario instead of the Dark Lands.
Peach isn't already trained as a warrior-she learns alongside Mario, with Luigi helping in his own way.
The Koopalings appear as Bowser's elite generals instead of being absent.
Donkey Kong initially refuses to help Mario until they both fight a common enemy sent by Bowser.
The Mario Kart battle on Rainbow Road is longer and features more enemies from across the Mario series (Shy Guys, Koopa Paratroopas, and Lakitus).
Pauline is given a larger role as the Mayor of Brooklyn, helping the Mario Bros. set up their plumbing business in the beginning.
Yoshi joins Mario and Peach's group after escaping Bowser's army, not just a cameo at the end.
The Super Star isn't the only power-up-Mario, Luigi, and Peach use Fire Flowers, Tanooki Suits, and Ice Flowers during the final battle.
Bowser's wedding plan involves merging the Mushroom Kingdom and Dark Lands into one empire rather than just forcing Peach to marry him.
Instead of being shrunk and trapped in a jar, Bowser is sealed away by the combined power of Mario, Luigi, Peach, and Yoshi until a sequel.