Racing tires are made with specially formulated rubber compositions that are harder than regular street tires. They also have similar nylon and steel cords between the outer rubber and inner butyl liner. The rubber in racing tires is harder than the rubber in street tires because the forces generated in racing applications are much greater than those generated in regular street driving and the speeds encountered are very much greater than on the street. The type of racing application will determine the exact composition of the rubber in the tire. The surface being driven on will also determine the composition of the rubber used. The exact chemical compositions are usually considered proprietary secrets by the tire makers.
For more info, see Finding the Right Aftermarket Tires for You