While some say the release (has an element of long leg short leg) of the downhill ski from its edge while wedging will cause an active weight transfer to the uphill ski and steer you into the fall line my experience is somewhat contradicting. Its because the wedge only works if you have the two skis pushing against each other OR significantly more pressure on your outside ski. As you wedge across the slope your CoM will be located more over your downhill ski. That is where the pressure is. That is where you weight is. The steeper the pitch of the slope and the more across you go the more significant this effect will be. So releasing that downhill ski will in most cases not shift the pressure from your released downhill ski to your uphill ski since the force caused by your edged downhill weighed ski will instantly go from dominant to cero and release your CoM in the direction of the fall line. Result: skidding the downhill ski sideways while the uphill ski is still on its BTE and edge locked.
The proper way of wedge turning IMO is by combining the inside ski release with an active weight transfer. First you shift your weight out over your uphill ski and as you start turning into the fall line you release that inside ski gradually from its edge. You don't want to release it too much because you want the ski to stay on its inside BTE and as you come past the fall line and the pitch of the slope turns around on you the angle of the inside ski will be automatically reduced and the ski released. For demo purposes gross movements can be used but as you become more comfortable with wedging this way, smaller movements are used. By using this method you can wedge turn practically anywhere. That builds your confidence and boosts your enjoyment. And the student only needs to concentrate on one movement that is easy to understand. Especially children and very careful adults.
I did some myth busting. Came to the conclusion that the Gliding Wedge concept with the Passive Weight Transfer did not work sufficiently well for my taste. So why does it work? Its quite simple actually. You have basically two options: You mask the active weight transfer skilfully or you use excessive rotary of which the latter is offcourse the wrong way of doing it. Sad to say its also the most common. Not only in the gliding wedge concept but in most wedging demos. What you want to do is the total opposite of staying square and rotating your upper body into the turn. You want to Counter Rotate your upper body towards the outside of the turn. Rotation into the turn leads to Banking and Hip Rotation and flattens the edge angle on you outside ski causing inefficient turning and sideways skidding. Bad stuff.
Once you advance to parallel skiing the only difference will be the turn initiation. In the wedge only a weight transfer is needed while when skiing parallel you need to pivot your skis slightly at initiation. But all the rest is the same. Angulation, outside ski pressure, counter rotation and a round and even turn. The only slightly problematic thing would be the extension bit. If you want to extend into the transition you need to flex before that. In some of the classical applications you flex through out the whole turn in order to be able to extend into transition. This is not optimal since you want to extend into the turn for better stacking. Especially when carving. Or when skiing bumps. That's what bump skiing and carving has in common. I go for a slightly different style where I flex momentarily just before the initiation. But my movements are very subtle at the advanced level.