In 'Normal' steering is light. When you press the flappy paddle it switches to 'Manual' (M1/M2/M3/etc) for about 8 seconds and then reverts back to 'Drive' (D1/D2/D3/etc).
In 'Sport' steering is heavier, suspension, and gearbox are slightly more responsive. When you press the flappy paddle it switches to 'Manual' (M1/M2/M3/etc) for about 8 seconds and then reverts back to 'Drive' (D1/D2/D3/etc).
When you push the gearstick over to the left it enters 'Sequential' mode (S1/S2/S3/etc). Gearbox is MUCH more responsive and aggressive. If you use the flappy paddles in this mode it will changed from 'Sequential' mode to 'Manual' and stay in that mode until the gearstick is moved back to the normal position.
Hope this clears things up.