Wind Waker is much, much more complex than the DS games. You have a tremendously bigger overworld with a lot more dungeons, NPCs, items, etc. It's a lot closer to the other 3D games (Ocarina of Time, Majora's Mask and Twilight Princess). There is a deeper story that hails back to an earlier game from the series.
Basically, it's the same Link and the same Tetra from Phantom Hourglass, but obviously before that. It starts on Link's birthday, but before long he's on an adventure that leads him all over the ocean. He will meet fairies and wind gods, sages and kings, dragons and, well, see for yourself. While it has its weaknesses (there's a particular drag in the second half of the game), it's without a doubt one of the best Gamecube games ever released, and you should find a way to play it.
Soon.