Compounding - using a compound to remove paint imperfections, oxidation, scratches, stains, and other belmishes.

Cutting - same as compounding, just a more specific term. "Cutting" means using an abrasive to "cut" into the paint finish.

Leveling - Smoothing out a paint finish by cutting the "peaks" down to the level of the "valleys", thus "leveling" the paint finish. This is usually necessary on fresh paint when it has orange peel.

Buffing - This generic term can mean literally anything from compounding to wiping the wax off by hand. It simply depends on who you ask.

Polishing - using a mildly abrasive polish to do one or more of the following: remove swirl marks, restore color and gloss to the paint, and/or remove minor paint imperfections.

Swirl Removing - using a mildly abrasive polish to remove swirl marks. Sometimes a compound is needed to remove severe swirl marks.

Waxing - Applying a wax

Sealing - Applying a polmer paint sealant

Note: Many products marketed as waxes do not really contain any natural waxes such as carnauba. They use synthetic waxes, polymers, resins, etc. In other words, they are really closer to being sealants than waxes.