First things first - the fundamental difference between shaving with an electric shaver and a manual razor is the way the hair is cut and the preparation techniques needed.
With a Razor, the hair is cut with a single stroke of the blade. While with an Electric Shaver, the hair is cut between two blades like the motion of scissors.
Traditionally a razor requires a wet shaving technique while the electric shaver usually requires a dry shaving technique. You can read up on the differences between wet shaving and dry shaving here.