Actually, the various grades of polish are designed to get what the previous left behind. A coarse polish, is like wetsanding, but I think the grit is usually closer to 2000-3000, don't know for sure. The coarse polish is to remove major defects and severe oxidation.
Then you have a medium abrasive polish, designed to remove swirl marks and other micro marring. The course polish leaves swirl marks, the medium polish takes out swirl marks.
Then you have your fine/finishing polish. This adds additional gloss by taking out the ultra fine defects. You can't really see the defects, but you can see the difference. I use the Klasse AIO for this. It is both a fine polish and a paint sealant.
Glazes, IIRC, usually contain fillers, so they can be used after or in place of the fine/finishing polish. I haven't used them because I didn't see a need to buy them, and my paint is cheap. The guy who painted it did a crap job.
A pure wax does not do anything to swirls, scratches, etc. It is simply a layer designed to protect and dazzle. If you had swirls before you applied wax/paint sealant, you will have them after.
Foam pads are definately less abrasive than wool pads, but the purpose of the foam was for a way to detail a clear coated paint. Wool pads are too abrasive, and are usually used as a step above the coarse polish. They do make finer wools, and it used properly, can be used on clearcoat paints, but that takes a professional detailer, or someone with years of experience.
So, you can use polishes all the way up to the wax/paint sealant step. A glaze isn't necessary, but will yield a better looking finish (although after the fine polish, "better" is neglible). Let's save this for another thread though...
Polishing Paint to Perfection - Autopia Car Detailing Forum
Article is a little contradictory (however it's spelled) since they mention glaze, which they call a very fine cut, but don't say to use it. My info is from other detailers on that site. They have very many knowledgeable people, and the reason I have my PC.