Eau de Cologne is a local trademark for "Kölnisch Wasser" Cologne, Germany.
EdC is the term used today to refer to a perfume solution with ~ 3%-5% essential oils in an alcohol and water base.
Eau de Toilette (EdT)
~ 6-10% essential oils in an alcohol and water base.
The differences are simply a matter of the amount or concentration of oils in the fragrance. These oils are called "juice." The highest concentration of "juice" is in perfume (or parfum). Next would be Eau de Parfum, then Eau de Toilette, and finally Eau de Cologne.
After Shave has the least amount of oils. The higher the concentration of "juice" the longer your fragrance will last, and the less you need to apply.