What are the different types of skiing?

If you are talking about brands, Head, Salomon, K2, Rossignol, Nordica. If you mean styles of skis, park and pipe, all mountain, powder, race and performance. The difference between race skis and performance skis is that race skis are made for racing on a race track for a professional, performance skis are made to use on regular runs at fairly high speeds for the advanced to expert recreational skier.