A coating is a covering that is applied to the surface of an object, usually referred to as the substrate.
The purpose of applying the coating may be decorative, functional, or both.
The coating itself may be an all-over coating, completely covering the substrate, or it may only cover parts of the substrate.
Paints and lacquers are coatings that mostly have dual uses of protecting the substrate and being decorative.
Although some artists paints are only for decoration, and the paint on large industrial pipes is presumably only for the function of preventing corrosion.