Reflecting a little further on this matter, including some of the stuff from Doby earlier...
Crossunder/over is only concerned with the lateral displacement of each other.
"retraction" to me is a description of the vertical disposition between the CoM and BoS that is not necessarily reliant on their lateral disposition.
I do agree with you that flex to release isn’t necessarily going to constitute a crossunder turn. I don’t use flex to release but,..
...Regardless of that, with the right skills and mobility, we aren’t even “releasing” our CoM in “short’ turns at all.
Just like an expert zipper line mogul skier whose CoM rides straight down the fall line with almost no lateral displacement to speak of. For an advanced short turn skier, releasing the CoM for a “flex to release” move doesn’t even happen.
Ok, so its possible that the word release here is not being used consistently. I don't really care about identifying some particular "correct" use of the word...as far as I'm concerned, if you can get your point across then it works. We often see confusion in these discussions, for example, when using the word "release" and not clarifying if its the skis or the CoM that is being released. Two different things. They are both a type of "release".
Here I can see yet a new releasing distinction that perhaps needs to be made...
I see here two different CoM release concepts being slightly conflated in the discussion. One is the concept of releasing the CoM through transition to allow it to
move/flow across the skis in crossover.
It facilities continuation of movement. That's the concept that I personally I am usually talking about.
But the kind of release that I think Doby is describing here is a bit different, he's talking about actually
stopping the movement of the CoM side to side across the hill by releasing the impulse energy harvested at the apex with deep flexing of both legs, which halts the CoM's lateral movement and allows the skis to zip across without having to push the CoM there.
Two different things really, though both do involve flexing or relaxing the legs, with subtly different timing in terms of muscle relaxation in two different legs at different parts of the turn.
Regarding the super short radius turns you identified, where the upper body appears to come straight down the fall line without displacing side to side across the hill: In this type of turn, the skier is releasing the impulse energy before it moves the upper body across the hill, instead that energy zips the skis across. Absolutely. When we see what looks like high energy cross under, there is a lot of that happening. However, it still may or may not mean the skier is flexing to release their CoM with the other kind of release, which is to allow the CoM to move and flow down the fall line and crossover the skis. If they don't release their CoM to crossover, then they will have a lot of pivot. If they want higher performance they will also release their CoM to move, flow down the hill into the next turn, which will enable a more carve-pure turn entry and rounder SRT turn shape.
Both types of releases absolutely can be done in the same turn!
The subtle difference is the timing and muscle relaxation used in each leg.
WHEN you release the forces and how you do that between your two legs in different amounts at different times. Relaxing and flexing to release the old outside leg at a certain timing in the turn allows the CoM to move/flow across the skis into the inside of the next turn. The old inside leg is typically already flexed. Allowing it to flex even more does not contribute to this crossover, but it could contribute to halting side to side displacement of the CoM, allowing the skis to zip across in crossunder instead. Also relaxing the outside leg late can contribute to harnessing more of the impulse energy from the apex, and it also slows down or halts the transition crossover of the CoM.
So these factors all contribute to some interesting combinations of things that can happen when you use flexion to release, depending on the timing between inside and outside leg and where in the turn it happens.
What I typically see with peers attempting to do so called "retraction turns" as something they don't normally do, they will relax the old outside leg late (harnessing as much apex impulse as they can, but also reducing or eliminating crossover movement of the CoM, and then they will retract both legs deeply, having lost their crossover movement...the skis do cross under, and will almost certainly pivot because they lost crossover movement. It doesn't have to be the way though,
its possible to get just the right amount of cross under without losing crossover.
Typically in SL they are
WANTING to displace the CoM sideways across the hill, and I would claim this is the harder skill in SL sized turns. That means they need to harness the impulse energy from the apex to not necessarily cross under so much, they need the skis to push their CoM across the hill also. Why then are they flexing so deeply through transition in many cases? Lots of times they are just trying to get to the new edges ASAP. The shortest path for the CoM can take means shortening the legs, but they are also being careful not to actually release too much of that apex impulse energy..they want it to displace them across.
Again watch these videos from TDK closely... From this Camara angle is really hard to see the crossover because that movement happens towards the Camara. A side view would show it more. But you can still figure out whether its happening by looking at how the skis are tracking. If the skier gets to the new edges without a pivot, then crossover is happening and that means they flexed to release (in the sense of allowing CoM to move/flow across the skis)... And we really have no idea when each of their leg muscles is actually relaxing, we can only draw conclusions of what we think they are doing based on the outcomes if we know what to look for. To some extent you can watch each leg very carefully to see which one is in the act of flexing or extending at any given moment of time and make some determination about how and when they are relaxing their muscles in each leg to allow things to happen.
Bottom line, flex to release does not necessarily mean its categorically a "cross under" turn. I think many people that are stuck on that notion will tend to miss opportunities to explore what is possible through downhill leg relaxation and release to cause movement of the CoM to crossover.