The distinction for the two words you are referring to is with regards to the complexity of the circuit which uses electricity.
A flashlight is a very simple system. It doesn't primarily feature integrated circuits or digital logic or any advanced circuitry. It uses electricity thus it is "electric".
A computer is an extremely complex circuit. Most people can't begin to grasp the concept of a CPU from the perspective of a current-flow device. An electrician can't just hook it up to the power mains.
At some point along the complexity spectrum a device ceases to be merely electric and becomes electronic. Note: I think this also requires integrated circuits and the like. I don't imagine that anyone would refer to the power grid as electronic (though some components of it are).
Consider these cases:
- An electric chair
- An electronic chair
The first is a chair which predominantly features electricity. The second is a chair which has some feature made of a complex circuit (for example, the seats in cars which are automatically-adjusting).
- An electric toaster
- An electronic toaster
The first is a run of the mill toaster. The second is a toaster that lets you program in an image to burn into the toast, and which sends you an email when the toast is done.