Why would there be differences? I understand than in a running VJ there are forward vectors of movement that determine different loads on different muscles than in a simple, stationary squat, but other than that? Maybe the fact that in a squat you stop at the top and not fully extend and leave the ground as in a jump, hence the hip extension (or hyperextension) part doesn't occur.
And yeah, I know what you say Andrew. You're basically choosing the same point in squat to go up as a VJ would have (at least for you). So basically it's repeating the same ROM, with the coupling phase in the squat occuring at the same depth as it would occur in the VJ (functional training).
But then you say
"so going deep is more of the quads not being able to do their job, which, at that depth, is of course not there job, it's the glutes job"
If that's true, then maybe we need to focus more on the quads so that they ARE able to to their job, so you bend less in a jump, spend less time on the ground, and all the positive influence these things have on a VJ. If that's true, then you're always going to be limited by the quads, since you don't need the glutes as much if any when you barely bend to 1/4 when you jump.