Paint correction is the process of buffing and polishing your car's paint, removing the swirls (spider-webbing), holograms, a haziness or any other defects in the paint.
Buffing and polishing are two different things, using different machines or in some cases by hand.
On light-colored cars, swirls, holograms, and other paint blemishes aren't that noticeable but on darker colors, they stand out like a sore thumb.
Paint correction can involve multiple steps, usually referred to as steps or stages. This is where you would go over the paint surface once with a buffer and compound, first step. Then going over the surface with a polisher and polish, second step. You can continue this process using finer and finer compounds and polishes until you achieve desired results.
The buffing/polishing process can usually take anywhere from 5-40 hours.
This is a single step of polishing that will improve the surface returning some of the gloss to the paint and in the process remove minor swirl marks.
This type involves two steps using a buffer and polisher. The first step, usually called the compounding stage, is with a buffer and compound to remove swirl marks and some deeper scratches. This is then followed by a polishing step to remove any hazing or micro-marring from the compounding step.
Moving even deeper into paint polishing is multi-step buffing/polishing. This involves multiple steps of compounding to remove as many deep scratches as possible without compromising the depth of your car's clear coat.