Priest, sorry to hear that there is no youtube for you guys but maybe you are better off that way. Anyway, the S shaped versus the Z shaped turns do not tell us if they are carved or skidded. It only tells us what kind of shape the turns have. If turns are nice and round or if they are uneven with lots of sideways skidding. If you are not carving your turns they can be eather S shaped or Z shaped depending on your skills. A good skier can controll the edge angle and the skid so that the turns become nice and round while a lower level skier rushes across the fall line with too much weight on his inside ski and lets his hips rotate outwards in the turn making his ski tails loose gripp and brake out more than necessary causing eccessive skidding and resulting in a Z shaped turn. However, if you truly carve as in "slicing" then the turns will be S shaped because the skis turn according to the skis side cut and there is no skis skidding sideways. Only forward motion of the skis.
Some will tell you that there is no such thing as a cleanly carved turn with no skidding. This is probably true if you abandone skiing and start acting like a sciantist but the fact is that there is a huge difference between being able to carve as in slicing or if you are letting your skis skidd. Also be aware that the word "skidding" has no unanimous meaning. It can mean lots of different things to different people. Im in the camp that calls non carving turns skidded turns. For others skidded turns are divided into many more subcategories including such terminology as carving, brushing, scarving, feathering etc. leaving skidding as a bad such skiing. Confused, dont be. Just keep on posting