Lets check out what wiki has to say about steering:
Steering the term applied to the collection of components, linkages, etc. which will allow a vessel (ship, boat) or vehicle (car, motorcycle, bicycle) to follow the desired course. An exception is the case of rail transport by which rail tracks combined together with railroad switches (and also known as 'points' in British English) provide the steering function.
How about this:
Steering the term applied to the collection of components, linkages, etc. which will allow the skier to follow the desird course. An exception is the case of carving by which ski side cut combined together with body movements provide the steering function.
Conclusion is that the steering angle and the skidding angle are two completely different things. Steering angle is the angle between the direction of the CoM and the direction the ski tip points. The skid angle or better yet the "side slip angle" is the ski angle relative to the snow flow. Carving would be steering. Steering angle cero. If the tails brake lose the skis would be over-steering. Now steering angle would be greater than cero.
If we look at aeronautical vehicles for a reference they normally turn so called "coordintaed" turns. If we have any pilots here please correct me if Im wrong. A coordinated turn is when you roll the airoplane sideways. Annother way of turning would be skid-to-turn where the plane is placed at a sideslip angle relative to the airflow. Check this out:
Skid-to-turn is an aeronautical vehicle reference for how such a vehicle may be turned. It applies to vehicles such as aircraft and missiles. In skid-to-turn, the vehicle does not roll to a preferred angle. Instead commands to the control surfaces are mixed to produce the maneuver in the desired direction. This is distinct from the coordinated turn used by aircraft pilots. For instance, a vehicle flying horizontally may be turned in the horizontal plane by the application of rudder controls to place the body at a sideslip angle relative to the airflow. This sideslip flow then produces a force in the horizontal plane to turn the vehicle's velocity vector. The benefit of the skid-to-turn maneuver is that it can be performed much quicker than a coordinated turn. This is useful when trying to correct for small errors. The disadvantage occurs if the vehicle has greater maneuverability in one body plane than another. In that case the turns are less efficient and either consume greater thrust or cause a greater loss of aircraft specific energy than coordinated turns.
I think that parallels to skiing can be drawn big time. Coordinated turns would be so called carved turns. Mabye we could replace the word carivng with the world coordintated alltogether. Skidded turns could be eather skidded or side slipped. If we look at the wiki here above we can read a very cool description of skidded (non carved (coordinated)) turns: in skid-to-turn, the skies are not rolled to a preferred angle. Insted commands to the control surfaces are mixed to produce the maneuver in the desired direction.