I'm wondering if we can have a discussion about differences in these two conceptualizations, the intents that accompany the two concepts, and the differing actions a skier takes as a result of each. And why we sometimes choose to use one concept rather than the other.
Sorry for what will be considerable overlap with what others have said.
Of course
technically it makes no difference to the movements the skier should make. But I can imagine that introducing the concept of skiing apex to apex could beneficially alter the mindset of many skiers.
Alpine skiing is at the core about moving downhill. Yet many novices have a horror of the fall line. If one describes the goal, the end point of turning action, as getting to moving straight downhill, it could help overcome that. (Sure, we know there's actually no end point.) If that's too scary, back off to gentler terrain. The purpose of turning is to create the amount of offset needed to move from going downhill in one place to moving downhill in another place. No more offset than needed, no less. (Racers would agree.)
Many skiers, some well past the novice stage, approach turning as something you do to get from one traverse to another. But traversing isn't real skiing. A focus on getting to the traverse leads to hurrying the turn with pivoting moves. More insidiously, as a skier advances, it leads an interruption of downhill flow, between "turns." It's difficult to start a good turn from a traverse. What I see many developing skiers failing to embrace is the importance of allowing the COM to move continuously downhill, separated from the more across-the-slope path of the skis. If there's a static point in the turn cycle, the skier will have to start all over with moves to reestablish that downhill flow of the COM, and then it will take a turn or two to be able to get more dynamic.
So if it can be drilled into a skier's mind that getting sideways across the slope is not an end point, but merely one point along a sinuous path, perhaps it would help overcome these negative movement patterns.