When you use the shift paddles in S, you are in complete manual shift mode (except for downshifts when coming to stop) and it will not go back to automatic shifting unless you go back to D. They call this manual sport mode.
However, when you put it in S, and don't touch the paddle shifters, it does put the transmission into an automatic sport mode where it stays a gear or two higher on purpose to keep you in a medium power band when going thru corners and what not.
When you use the shift paddles in D, it will go back to automatic mode pretty quickly if it senses you are done using the gear you manually changed to (whether to pass, run red light, engine brake down a hill, etc.)
I haven't been able to notice a difference when using the sport or track mode switch, but I think it might be more related to traction control settings. And the S on the shifter is more of the sport mode of just the transmission and it's shifting behavior.
I played with my driving mode switch today for fun, and sport mode does affect the transmission shift points the same as putting it into S on the shifter. So in that regard, they do the same thing, but using the paddles in full manual mode requires the shifter to be in S.