When you polish surfaces you use the coarser compound first. Some people (most) will stop at that point. To do it right you need to go to the next step which is using a glazing compoud like the Finesse-it with a foam pad not the wool. This removes the fine scratcthes from the compound and truly polishes the surface. It's hard to tell on white however on something black you'd see the difference.

If you don't glaze it the shine will seem to fade faster and stain easier. The finesse-it is a good product but the best that I've used is Meguiars #7 show car glaze applied with the foam pad at low speed.