You can only have S mode for the gearbox if you are in Sport (as far as I'm aware).
When you put the car into Sport mode, by default the DSG gearbox goes into S mode (selects lower gears and hangs on to the gears longer, with higher revs before changing up during acceleration). You also get the full throttle response and the loud fake engine noise.
If you want the throttle response of Sport but not the gear change attributes of gearbox "S" mode, you can pull back on the sprung gear stick position of "D" to change "S" to "D". You will see this in your dash info as S1 would become D1 (for 1st gear), S2 becomes D2 etc. Similarly, if you are in Eco mode, you have E1, E2, E3 etc.which change up very early and labour the engine.
Sport mode with D gearbox mode is no thirstier than Normal mode with D gearbox mode - you just press the pedal less to get the same response from the engine.
So you've got a Polo GTI, the full travel of the throttle pedal gives you access to the whole 200ps power.
You stick it in Normal and you have somewhere in the region of 75% of the power across the pedal travel (but if you floor it and press into the clicky part of the accelerator pedal then this gives you full throttle).
Similarly, you stick it in Eco mode and the response is blunted further, with maybe 50% of power available across the pedal travel.
With Eco you gain coasting mode, which will give you modest gains and the Eco mode of the gearbox making changes up happen very early. In Normal and Sport there is no coasting mode.