Really there is not much difference. They come from different kind of buttons, turn off - a twist is needed to turn it off (like a Dial, or a Knob). Switch off - a push is needed to switch it off (like a light switch that has only on / off) But the meaning is so close that they are probably always interchangeable.

There's no difference in meaning. "Turn off" is more common in U.S. English; I think "switch off" might be British. Both mean "to de-energize" and there are no subtle differences in meaning. Idioms sometimes persist when technology changes.. As Neil says, "turn off" emphasizes the turning motion of the control, "switch off" emphasizes the electronic function of redirecting a flow. It's my GUESS that the phrase ""turn off the light," and might well go back to the days of GASLIGHT, when you turned off the light by turning the handle of a valve. Early electric lights tried to imitate the familiar gaslight and worked the same way--a turning handle directly underneath the light fixture itself. Wall switches that let you turn on a light as you entered a room and "unroll a carpet of light ahead of you" were a GE innovation of the 1920s! Before the digital era, it was universal for electronic devices like television sets or phonographs to have a combined volume and power control operated by a knob; you "turned down" the volume by rotating the knob to the right, and when it was all the way down there was a slight click and you "turned off" the power. "Switch off" to me invokes a mental image of a railroad switch, where a train can be guided onto on track or another, and then by extension to an old-fashioned electrical "knife switch" (do a Google Image search to see what that is), and then to anything that controls electrical power. In the digital era, the price of the traditional turning knob for controlling volume became relatively too high--much cheaper to control volume with button pushes or touchscreens--and we no longer "turn" a device off. However--getting back to "there's no difference"--"turn off" is just an idiom and nobody even processes the word "turn" unless they are thinking about phrase origins.