I don't know if your question has been answered to your satisfaction yet, but you have stimulated some good discussion!
I'll try another description here, for what it's worth. Let's use the analogy of SKIING and RUNNING. "Running" is an activity that involves a lot of different movements and "techniques," most of which we make without even thinking about it. Sometimes we run fast, and swing our arms vigorously. Sometimes we just trot along gently--or walk. Sometimes we speed up, and sometimes we slow down--and either can be sudden or gradual. Sometimes we change direction, again quickly and sharply, or smoothly and gently. Sometimes we run on a smooth, hard surface, other times on soft or irregular surfaces.
Every one of these different options, and each combination, involves a different "technique," although they ALL fall under the category of "running." And they can all be done with varying degrees of skill and ability. Surely, there are "common threads" that run throughout all the variations, but there are also significant differences. To be a good runner, it is important to become adept at all of these "techniques." And very few of these things would normally be called "turns"!
Like "running" and "turning," "skiing"
are not the same thing, despite common use of the termsand conventional wisdom! Turning is only a small subset of the "things" we do on skis.
But we do TURN, by my much more restrictive definition, to the best of our ability, WHENEVER our intent is to control direction on anything but a straight line. Regardless of skill level--from expert all the way to "never-ever" beginner--the intent to contol line will bring out a blend of rotary, edging, and pressure control skills that is fundamentally similar. The same is true when the intent turns to "braking"--the movements, regardless of skill level, will suddenly become very different from the movements of turning, whether the skier is conscious of the changes or not, and whether the skier still calls it "turning" or not.
Experts will do it skillfully. Beginners will do the best they can. But if the intent is the same, the movements will share some basic, qualitative similarities. If the intent is to turn--to "go where I want to go"--all movements of my body will tend to be in the direction that I want to go. Ski tips will turn in that direction--inside tip first. Skis will tip/roll in that direction, releasing their edges then re-engaging to provide the "traction" to push my body in the desired direction. My body will move in that direction, possibly directed and enhanced by movements of my arms and poles. To go left, everything moves left, to the best of my ability, and with an intensity proportional to how quickly and vigorously I want to change direction. I call these movements in the direction I want to go, "positive" movements, regardless of what body part or piece of equipment they involve. In a "turn" (defined as "an attempt to go where I want to go"), all movements are "positive movements."
But that offensive "GO" intent is surprisingly rare in skiing. Rarely does it matter that precisely, outside of a race course, a treed glade, or a very crowded run, where exactly my skis go. A more common intent for most skiers is the desire to control speed, to resist the pull of gravity--to BRAKE.
If I want to BRAKE, suddenly all those positive movements become wrong! Braking involves just the opposite type of movements--NEGATIVE movements--movements AWAY from the direction I want to STOP going. Because this defensive intent rules 99% of most skiers' "turns" (or should I say, 97%?), most skiers make largely "negative movements," again regardless of skill level. Beginners brake with little skill. "Experts" brake skillfully (although as we've discussed, true experts have also discovered that skillful and intentional control of line--TURNING--skiing the "slow line fast"--minimizes the need for braking in the first place!).
Of course, there are plenty of times when we need to control neither direction nor speed. Wide-open runs with "comfortable" pitches (whatever that means to the individual skier) allow us the luxury of just playing. This is where we can just tip our skis and enjoy the sensuous play of g-forces, floating, and weightlessness of the "pure-carved turn"--or the exhilarating rush of terminal velocity. These intents too produce different kinds of movements--different "techniques"--different "types of turns."
And a situation where neither direction nor speed needs controlling also presents the ideal environment for trying or practicing "new movements." Without our control--or our life--depending on them, we can explore new movements at will. But of course, lacking any particular intent, none of these movements is either "right" or "wrong."
The point is that we really don't have to worry about which type of "turn" is "correct." Our intent will govern our movements absolutely, regardless of our thought process or our desire to make any particular type of turn. This is why so many lessons fail--the instructor tries to teach a certain type of movements to a student with a conflicting intent! The instructor who tries to teach "release your edges and let your skis dive down downhill" to a skier who wants only to brake and resist the pull of gravity CANNOT SUCCEED! And all this talk of "which type of turn is 'correct'?" is actually irrelevant. Intent dictates the type of movements we make, whether we "choose" that or not!
Want to make "Center Line" (PSIA trademark, by-the-way) turns? You will, whether you know it, or want it, or not, if you try to follow someone else's tracks. Put yourself in a situation where your intent is to contol line, and your movements will fall somewhere on the "Center Line" even if you've never heard of it! The "Center Line" simply represents what those movements tend to look like, and identifies typical "milestones" along the path of skill development. At a low skill level and a very low speed, most skiers (and yes, this includes both the students AND THE INSTRUCTORS of "direct parallel" schools) will tend to show a gentle "wedge" as they try to turn both skis in the direction they want to go. As speeds increase, the same intent and same fundamental movements will tend to "match" (become parallel). We don't "teach" wedge turns or wedge christies--we simply recognize that they happen!
If you become defensive, regardless of your level, "negative movements" will creep into your skiing. Rather than releasing your edges and turning your tips downhill, you will keep gripping the mountain and push your tails uphill/out of the turn/into a skid to start a "turn." Parallel "turns" become hockey stop-like skids. Wedge christies become stem christies. Razor-carved tracks quickly vanish as the edges scrub away speed.
So the TYPE of "turn" we make is a function of our intent. The QUALITY of the turn is a product of this intent combined with our ability and skill level. "Style" is the personal flair and expression that each of us adds on top of these things, representing our individual personality, anatomy, attitude, and habits.
Again,There are many good ways to get down a mountain on skis, but very few correct ways to make a TURN!
It's all good....