If you are confused about the difference between polishing a car and waxing a car then this article should help you understand the difference between the products and processes.
Polishing of the paint surface is used to fix defects and can be either chemical or abrasive. Chemical polishes include things like Dodo Juice lime prime and Collinite Pre Wax Cleanser which chemically clean the surface to remove contaminants and defects. However they are only used for surface preparation and will not remove swirl marks. Clay bars are non abrasive and are often used prior to polishing to remove stubborn deposits on the paintwork. A clay bar will lift the deposits off the surface and embed them into itself. Once the deposits are embedded in the clay its safe and it wont scratch your car. Do not forget a good quality lube to use with the clay to reduce friction and prevent scratching your paintwork.
To remove swirl marks an abrasive polish is best. There are plenty of Polishes around which will do the job. Abrasive polishes need a machine to reach their full potential. Either a random orbital, forced rotation or a rotary.
Once the surface is prepared then you are ready for waxing which is usually the last step you do when washing or detailing your car. The purpose of waxing is to create a barrier between your paint and the environment. Most waxes contain UV inhibitors to stop the sun damaging the paint. They also repel water which stops your paint getting etchings from watermarks.
Natural waxes tend to give more of a warm and a glow. These waxes range in price and there are various brands including Dodo Juice , Meguiar's, Collinite and many many more. Natural waxes also tend to bead water. This means the water forms tight little beads that run off very easily. If you have a freshly waxed car and drive it in the rain you will find the water will just run off. The lower end waxes and off the shelf waxes last 1-5 weeks before needing to be reapplied whereas the higher end can last 6-12 weeks.
There are also Synthetic products which do not contain wax. They, for the most part contain polymers or acrylic. These are the two main types of sealers. Sealants vary in price from brand to brand and durability will be different. Sealants give a different look to wax that is best described as sterile. The paint is shiny but it lacks the warmth and glow of a natural wax. Synthetics tend to sheet water. The water wont form beads, rather it will just run off in a sheet. Sealants leave a very slick and slippery surface. Sealants also last a lot longer than a wax with most giving at least 3 months protection and up to 12 months for layered sealants.