G'day Angie,
Although I have a slightly different stereo to you (I have aftermarket Bluetooth) I checked the operation of my iPod with both the normal iPod cable (USB output only) and the Hyundai iPod cable (with USB and extra jack). The iPod does work with just the normal USB cable, but the stereo treats it as just a USB, so it doesn't have the full functionality of the Hyundai cable.
The Hyundai cable enables you to drive the iPod (use folders, choose songs via artist/album/genre, etc) from the stereo. You can't totally drive it from the steering wheel controls, but you can go forward and backwards with songs in the playlist.
So in short, if you want the full iPod functionality from the stereo, get a dedicated Hyundai cable (or one from eBay). I paid $80 for mine from Hyundai, but you can get them much cheaper via eBay.
Hope this helps,
FatBoy