Race skis are designed to hold an ege on firm snow and very high speeds. These skis are bulky and are heavy because the extra weight helps dig into the hard snow of a racecourse. The ski has a narrow waist for a good edge and are fully cambered skis. These skis do not float well in fluffy powder. 

These skis are designed to be more recreational than racing skis. Just like race skis, carving skis are designed for groomers. These skis will excel in firm-groomed snow. When using these skis they feel like they will throw you from turn to turn. These skis are also good for a place where fresh snow is rare. 

These skis on the other hand are not typically used at a ski resort mostly because they are not the best for groomed snow. These skis come in a wide range of widths and lengths for different purposes and are generally designed to be lightweight for uphill skiing, but perform reasonably well for downhill skiing. Most alpine touring skis have early-rise tips to float in powder or soft snow, but camber is good for a good grip when going uphill. 

These skis are designed to hit jumps, boxes, and rails. These are also great for skiing backward because the tip and tail of the skis are completely identical, known as twin-tip skis. These are also designed to withstand taking a hard beating on boxes and rails 

Each region has a different weather pattern, snow conditions, and terrain options that make different types of skis more optimal. Big mountains that have a large snowfall every year (Around the U.S. and Canada) are best for rocker and wider skis, while on the West Coast heavy snow makes stiffer powder, so powder skis are better and can handle chop better. For firm snow and challenging terrain on the East Coast, all-mountain and carving skis are the best for those conditions. For the Midwest, there isn't a lot of mountain terrain or powder at all, so the best skis there are racing/carving skis or park skis for people who love tricks.