WOOL PAD - highly aggressive pads used for cutting or heavy compounding and removes extreme swirls or oxidation on very hard paint. It removes heavy oxidation much better than foam pads and generates less heat resulting in cooler surface. That said, wool is also safer to use on heat sensitive parts of your car such as bumpers and spoilers. The caveat is that it can leave buffer trails if you are not skillful enough.
CUTTING PAD - used for non-agressive cutting (moderate cut compared to wool pads). Use for removing buffing swirls or trails, oxidation and scratches.
POLISHING PAD - used for paint cleaning, remove swirl marks, light scratches, fine sanding scratches, and other defects in your car's paint.
FINISHING PAD - provides very little or no cut. Use for applying pure polish, wax, glazes, and sealant without marring the paint and produce a high gloss show car shine finish.
When choosing the proper pad for cutting or polishing, always make sure you match the aggressiveness of the compound/polish you are using with the aggressiveness of the pad. A mismatched combination creates unneeded work and waste your time and product, so make sure you have the right pad and polish for the job.