Cut and Polish is an old fashioned term for rejuvenating paintwork. It is actually a two stage operation, and may be more, if you want a truly excellent finish to your car's duco. Because modern paintwork is much softer, I prefer to call the process, Buffing and Polishing.
Paint technology has changed a great deal recently; some cars are now sprayed with water based paint and many colours are enhanced by spraying a clear coat over a base coat. On many newer cars you can actually see the true colour, before the clear has been applied, in the engine bay and inside the boot or fuel door.
Other cars, depending on the brand, age or country of origin may be painted with acrylic or enamel, with or without a clear coat, or even finished in metallic or pearl. There can also be vast differences in quality between different makes, country of origin, intended country of sale and factory or custom paintwork.
Be careful when buying any products labeled "Cut & Polish", it is normally a very abrasive compound and can quickly damage the paint if not used properly. Remember, it should be a two stage process and should therefore be two seperate products.
The key to successful polishing is patience, persistence and a gentle touch; not quick agression and abrasion. Most of the scratching on newer cars is in the clear coating which can be very soft. That is why your car loses its brightness after repeated washings - the clear coat is being rubbed and damaged.
Some cars show signs of Buff marks and Swirls, this is evidence of poorly executed cut, buff and polish work. Please be aware that there are some very clever products that claim to remove these - they are mostly just very fine filling polishes that offer a temporary fix and are only disguising a poor job. There should never be any of these patterns or blemishes in the first place!
There are also some very, very expensive polishes and paint protection products available. However, I fail to see the benefit of these because they are only truly effective if the paintwork has been properly prepared with specialist cutting or buffing work.
Be wary, also, of paint protection services and products offered to you when buying a new vehicle. They are a clever way of asking, "do you want fries with that" - that is, upselling, whereby increasing the car dealers profit margin. Any repair work, or colour matching or even buffing and polishing will often void your warranty for the product and I very much doubt the validity of, for example, a five year warranty. I would suggest you consider yearly attention by a professional such as Excell Buff to maintain a superior finish on your vehicle at a total lesser cost.