I am not sure but I believe the usual electric-fan switches its resistance value to change the power output.
Q1. With that case, does the resistor consumes the power?
Q2. Do switch #1, #2 and #3 consume same amount of power?
If the answer for both Q1 and Q2 are true, then turning the electric-fan to #1 doesn't save much energy compared to turning it to #3?
If we are talking about ceiling fans and regular desktop fans, then No, it is not a change in resistance. Check this thread for explanations on speed switches for electric appliance motors
Calculating the capacitor values to control ceiling fan speed
This thread also covers the topic in detail https://diy.stackexchange.com/questions/16620/how-do-i-shut-off-the-ceiling-fan-without-a-pull-chain
