Paint correction is the term most often used when polishing a vehicle's clear coat.
Swirl removal, scratch removal, etc etc....are all terms used. In essence, the clear coat is being removed to a level where its not refracting light...allowing for the paint to be more reflective and have a deeper look.
There are many different types of compound available now and I prefer meguiar's products. In addition to meguiar's there are products from Optimum, menzerna and others. Foam and wool pads are used with different compounds depending on the type of clear coat to achieve some level of correction.