The DS Download Play is a function that allows Wireless Multiplayer that was introduced on the Original DS. To do this though both players must have a copy of the game. On the DSi Nintendo created the Download Play menu so, it would be easier to do multiplayer.
Same thing but, different menu.
In Mario Kart
Mario Kart DS
Mario Kart DS has (obviously) a multiplayer function. If you select the Download Play function, you can race with your friend. However, you can only play on 8 tracks being Figure-8 Circuit, Yoshi Falls, Cheep Cheep Beach, and Luigi's Mansion. The other four are Retro Tracks, SNES Mario Circuit 1, N64 Moo Moo Farm, GBA Peach Circuit, GCN Luigi Circuit. Or more simply the Mushroom and Shell Cup. You also have to play as Shy Guy and drive in the Standard SG.