Simply: car wax is a filler, and car polish is an abrasive.
This means that car polish should be used when a vehicle’s paintwork is dimpled, dull, or oxidised. Polishes contain chemical cleaners of varying levels of abrasiveness that strip the very fine top layers of the protective paintwork layer to flatten or level the surface paint, often removing minor surface scratches. This leaves a shiny, polished effect. Not designed to protect, polishes are used to correct flaws in the paintwork by removing them. Car polishes also include gloss-enhancing oils that adds to the shiny finish of the polish.
Car wax however, is normally designed to protect a surface that has been previously polished by filling in any small imperfections that show up in a vehicles exterior in order to create smoother, more evenly reflected tone. Waxes are not abrasives, so waxes and polishes complement one another to produce a quality finish in the long-term. Car waxes are a combination of a natural waxes (most commonly Carnauba Wax) and other solvents.
Wax is naturally meant to be resistant to water, but car wax needs to be insoluble to oppose rain and washes of the car. As well as this, car wax can withstand high temperatures without melting or dripping off the vehicle.
Car polishes are abrasive, so using a high-quality polish means that when worked into the bodywork, the abrasive particles will break down more as it is manipulated into the paintwork.
Car polish is applied either by hand or by using polishing equipment after the vehicle has been washed. Car polish is put onto a microfibre cloth or the pad of an orbital buffer and applied in circular motions until the polish is completely disappeared.
Car wax is applied by putting some onto a microfibre cloth and smearing it onto the vehicle. Then you would leave it to dry for a few minutes and remove.