Transmission in S mode means that only transmission programs are altered. Essentially, the shift points are delayed so engine will rev higher before shifting up. And also, gears are limited to 1-6.

Switching to Sport mode from normal means:
1) Transmission will be in S mode.
2) Accelerator response will be enhanced (faster response)
3) Steering will be tightened. They claim to be more responsive instead of just being heavier.
4) For vehicles with IAS (mine), steering will be further enhanced (some IAS params also changed)

In short, switching the gear lever to S mode is NOT equivalent to standard settings in SPORT mode (missing the enhanced accelerator response).