^^That is well-described. Central has often had well-written technical material. Thanks,
@rcc55125, for posting it.
I identify two types of turn initiations that do not use extension.
The first is flexion turns, or flex-to-release turns. The other is retraction turns.
The turns described by PSIA-C are indeed "retraction turns" as I know them.
In flexion turns, the skier flexes the new inside leg to allow the CoM to cross over the skis. The new outside leg's extension is delayed. It progressively extends till skis reach the fall line, while the inside ski is used to guide the turn's path. Flexion turns do not have any additional flexion of the new outside leg at initiation (that leg is already flexed due to the old turn).
In retraction turns, both legs are shortened in transition, as described in the material above. This works as a down-unweighting move, so that the lightened or even lifted skis can be moved under the body to the other side of the CoM. Skis move much like a pendulum under the torso. They "cross-under" it. Rebound is part of retraction turns when they are done quickly. They are used for slalom-like turns with skier moving downhill in a narrow corridor, at speed. Retraction turns require some athleticism.
Of the two non-extension turn mechanisms, retraction turns are the less versatile method of motoring turns of the two. I am surprised that Central is choosing to promote this initiation method.
Flexion turns are quite versatile. They can be performed at slow or fast speed, in wide corridors or narrow, to produce turns with long, medium, or short radius. The skis do not get lift-off between turns due to unweighting. Flexion turns can be done with low energy, and take less effort than extension turns or retraction turns. Using flexion all day produces less fatigue.
The unweighting inherent in retraction turns can enable or even encourage the skier to push the skis out to an edge, which would be a no-no.
Flexion turns don't encourage pushing to an edge since they keep the outside ski solidly in contact with the snow and focus all the skier's attention on the actions of new inside ski, foot, and leg to shape the turn. I prefer to teach flexion turns to skiers as their first non-extension initiation.