Drive Select & S-Tronic Gearbox

When selecting economy mode in Drive Select the S-Tronic gear selection is prefixed with an E, instead of D or S. The Drive Select mode is also displayed underneath i.e. the word 'efficiency' is displayed in green. When the ignition is switched off, and then on again, the gear selection prefix returns to D while 'efficiency' is displayed in green. My question is whether there is a difference and separation between the 'engine mode' and 'gear box' mode? Can the engine be in efficiency mode while the gear box is another mode. Does this make any difference, compared to both engine and gearbox being in efficiency mode. Changing Drive Select to Comfort (or any other mode) and then back to efficiency causes the gear display to be prefixed with an E gain. To do this every time I get in the car is a pain. Is it necessary?