The hallmark of a friction burn is damage to the skin over a wide area. The area will be red, raw, and could be bleeding or weeping fluid. The biggest difference between a rug burn and road rash is how dry the injury is.
Rug burns are usually much drier. Road rash is more likely to weep. The difference could have something to do with the fibrous nature of rugs and carpets versus the harder surfaces of gravel and asphalt. Besides the obvious physical injury, the biggest symptom of a rug burn is pain.