It seems a lot of people, instructors included may or may not have you lift the ski to make that stem. I was under the impression lifting of the outside ski was optional, it was at first lifted and then later merely unweighted and slid over and the inside leg was in turn unweighted and slid over too. All just versions of a stem-Christie
Yes, I suppose that in a stem christie you don't technically have to lift the ski up off the snow (although that is the way I have usually seen it done.) Sliding or "pushing" the ski out away from the body is essentially the same technique -- you're unweighting the ski and moving it sideways to get it on edge, instead of guiding it through the turn. It's this "unweight" move that is particularly problematic, because if you're doing that you aren't releasing your old edges and allowing your COM to move into the new turn. It's a very defensive move.
Regardles of the terminology, with the old snow-plough stem-Christie, it was an edged outside ski that provided the turning impetus. It seems, from the little I have observed of modern teaching, that in the wedge turn, it is very much a rotational pointing of the ski tips in the direction you wish them to travel, turn your toes down the hill. This pattern of movement would slide right in to making a steered, non-carved (meaning not an edge-locked arc to arc) urn, the difference being the skis are in a wedge and not parallel, but still with a mostly flat ski and a strong torque applied about the axis perpendicular to the plane of the ski.
Could you confirm this is so, or if not, then pray tell what the main force driving the turn is in a gliding wedge turn or in wedge-Christie?
I want to say first that I've heard a few different versions of how this ought to be taught to beginners. So you may find some people who disagree with me on various points.
People just learning to make wedge turns are using a great deal of rotary and very little (if any) edging. I frequently tell people to "turn their feet towards where you want to go". Ideally the skis will be pretty flat, or with a small amount of edge on the outside ski. In practice, nervous beginners who are sort of flailing around and maybe sitting back too much can end up overedging both skis, and dealing with that takes some work. But you are correct in that it's mostly rotation of the skis driving the change in direction.
Once people have the basics down, I start working with them on getting their body to move in the direction of the turn, and making sure that the inside ski is flattened (or at least close to flat) and the outside ski has some edge angle. There's still a lot of rotary input, but you can start to take advantage of the ski's geometry by edging it and balancing more on the outside ski through the turn. As you are able to balance more on the outside ski, and are moving a little faster, you'll completely flatten the inside ski. Once you do that, the tendency is to reduce the wedge through the middle and bottom of the turn by straightening out the inside foot/leg (or just not holding it in a wedged position) -- a wedge christie.
Improving that further requires moving the COM inside the skis earlier in the turn (before the fall line). The earlier you're doing that, the more you can edge the outside ski and use its sidecut to help you turn. There's still rotary input being used to steer the skis, but you don't need it as much. If you move the COM far enough inside the turn early enough, you can start to get the inside ski on its inside edge as well -- and then you're making an open stance parallel turn.
In theory, it's a continuum. As your COM moves more into the turn, you get more edge angle on the outside ski, and if you balance more against that edged ski, it will turn more "on its own" and less because you're actively rotating your foot and leg. In that sense, the difference between a wedge turn, wedge christie, and open parallel turn is a matter of degree, timing, and better balance, not a fundamental change in technique.