Kinda, it also adds 3 new characters: wario, yoshi, and luigi. You unlock certain characters (mario himself, somehow, luigi, and wario) during portions of the game. Various missions require certain characters to be unlocked, but most of the game can be beaten with just mario. It also has some new levels too. It's a childhood favorite of mine, though best way to play it would be on 3DS or emulator cause the original ds lacked a joystick.
More and more I go back to the 3ds (well 2ds in my case) for playing the classics. With a grip it is just really comfy and there's a ton of games and rereleases for it.
Only issue I played Samus Returns (brilliant) and noticed if you need to ride the shoulder buttons for any length of time it gets crampy. But that's true of most handhelds.