Types of Terrain
Classic styled cross-country skis and skate skis are designed to ski on different types of terrain. Classic skiing is usually done on groomed, parallel tracks, but can be done on ungroomed, fresh snow as well as backcountry trails. In contrast, skate skiing terrain is more limited and can only be done on a groomed or packed snow surface.
Technique
Classic styled cross-country skiing is what most people picture when they think about cross-country skiing. Classic skis are designed to facilitate a forward kicking and gliding motion referred to as the diagonal stride. Classic skis are kept parallel to one another, and the skier glides forward by pushing off on the planted ski.
Alternatively, skate skiing is a newer form of cross-country skiing that resembles a movement more similar to inline skating or speed skating than classic cross-country skiing. In skate skiing the skis are held in a V-shape and the skier pushes the skis off in a skating motion to propel forward. Although the skate-skiing technique can be done on classic-styled skis, the classic technique cannot be done on skate skis.
Ski Features
The equipment used for the two different cross-country skiing styles is quite different. Skate skis tend to be shorter, narrower and lighter than classic-styled skis. Skate skis are narrower so they can glide quickly over packed snow whereas classic styled skis come in a variety of widths. Backcountry classic skis are going to be wider than classic skis intended for groomed tracks so that they offer more flotation on fresh snow. Skate skis tend to have less flex and camber (bend) than classic skis. Classic skis are cambered so that when one ski is weighted it grips the snow and allows you to push off onto the forward gliding ski.
Skate boots have more ankle support than boots for classic skiing because the ankle needs more support during the lateral side push of the skating motion. Skating poles are also longer and typically lighter than poles for classic skiing.