Kelly, you can't tell the difference, because there is no difference. They mean exactly the same.

Switch on is used when you have a switch (interruttore) while turn on is used when you have a knob that has to be turned (manopola)

Any electric appliance that has an on-off switch (or on/off button) can be "switched on/off". Eg. Switch on the lights/television etc. You can "turn on" any electric appliance, even if it does not have an on-off switch. "turn on" is also exclusively used for those with turning knobs; eg. turn on the gas, turn on the tap etc.

PHRASES switch on switch on the air conditioning: turn on, put on, flick on, activate, start, power up, set going, set in motion, operate, initiate, actuate, initialize, energize; toggle, flip, throw. switch off who switched off the fan? turn off, shut off, flick off, power down, stop, cut, halt, deactivate; toggle, flip.

You can say "you turn me on",but you can't say "you switch me on"