The screen of 'screen and recoat' fame, is a wire mesh that has abrasive particles embedded in it. It's similar to sandpaper. Unlike sandpaper, however, the screen has holes in it that decreases the total surface area. Thus it can have aggressive particles to grind off the damaged layers, but it grinds it at a lower rate so that the total surface removed is done at a slower more uniform rate.
The goal of a screening is not to remove the wood top surface but to remove the top finish layer so that the finish can be reapplied. For an even more gentle removal, sometimes softer pads are placed between the screen and floor. The screen and recoat process should be thought of as a routine maintenance procedure as opposed to a repair. The finish is a protective layer that is designed to be removed with wear and tear, that's why it's important to replace on a routine basis. If it is not replaced the hardwood itself could be damaged. Consult with a professional to determine if your floors can be recoated or if they need to be sanded.
Floors that have been finished with waxes or acrylic waxes can not be screened and recoated. Silicon cleaners and oil soaps are likewise not going to be recoatable. The wax, oils and soaps are so invasive that there will still be residuals that make the polyurethane difficult to bond with. If you have a floor that has an Aluminum Oxide coating, often found in commercial hardwood installations, you are not going to be able to do a screen and recoat. These floors need to be chemically etched before they can be refinished.