The differences are simply a matter of the amount or concentration of oils in the fragrance. The highest concentration is in pure perfume (or parfum). Next would be Eau de Parfum, then Eau de Toilette, and finally Eau de Cologne. Some manufacturers make a solid perfume, solid perfume is as strong as a pure perfume however it is in a gel-like consistency.
Eau De Toilette and Eau De Cologne are generally interchangeable, especially in Men's fragrances. After Shave has the least amount of oils. The higher the concentration the longer your fragrance will last, and the less you need to apply.