I’m starting this thread in order to discuss an idea that ski systems may not be so different as some may think. “good skiing is good skiing”, and that is no coincidence.
When you tip your feet you also rotate them laterally because how the foot joint is constructed. If you tip your foot and keep it pointing in the original direction you must also tip the tibia. This is what causes edging when you tip your feet. You can assist this foot/tibia tipping with muscles around the femur. This is knee angulation and in practice you use both muscles around the foot and femur to do this. Some systems focus on tipping the feet and some on pointing the knee, but they are quite close. The difference is primarily mental focus and how much you use the different muscle group. It is not good to overuse any IMO because it causes imbalance around the knee (overuse of hip muscles is much worse because they are stronger). A simple proof that you use both muscle groups is that most good skiers often end up unweighted and they still edge the skis purely. If they were using only the foot the knee would not move. If they were using only the hip muscles the ski would rotate in and down.
Most systems seem to agree that the best way to manipulate skis is edge and pressure management and not forcefully twist them. In one system you can e.g. initiate a turn by tipping the inside foot more than the outside and pull it back and thus let the skis brush. In another system you can initiate the turn by pointing the inside knee and keeping forward pressure. Again quite similar but described differently.
When the skis are up on edge you can enhance a turn by pressuring the tip sideways (in the ski plane). The only way to create this pressure is to counter rotate the upper part of the body. Most systems agree that this is best done via the hip/femur joint. In some system this is called counter acting, and in others it is called ILS or steering or counter (or a combination). I consider these actions to be active and they have a very similar biomechanics, but the focus is different.
There are also differences, but I think that a relatively large part of that is because of DIRT rather than fundamentally differences.
The big differences may be in how things are taught, and not the end results.