M = DxO Standard = Distortion / lens correction by optic module ON
VC1 = copy of M + VolumeDeformation diagonal
VC2 = copy of M + VolumeDeformation horizontal/vertical

VC3 = copy of M, but Distortion / lens correction by optic module OFF
VC4 = copy of VC3 + VolumeDeformation diagonal
VC5 = copy of VC3 + VolumeDeformation horizontal/vertical

all of them look different

comparing M vs VC3 / VC1 vs VC4 / VC2 vs VC5 show the lens correction
→ the lens correction is put on top
.
After having copied VC3 to 4 and 5, when I then activated the VolumeDeformation
the Distortion / lens correction was switched on ‘automatically’ and I had to take it OFF for them.

Q1 – I don’t think so. The lens correction (Distortion ON) seems to be separate.
Q2 – At least, it doesn’t mimic the correction for my lens.

I’ve used the diagonal VD with wideangle lenses.
The horizontal/vertical VD looks like the manual version of the auto one in Perspective.

note – I used some Perspective correction to have the pic properly centered.

I never thought that Volume correction replaced distortion correction. Volume deformation creeps in, when threedimensional objects are imaged on a twodimensional image plane. That deformation depends on the angle with which the light rays hit the image plane. The more pointed those angles are, the more deformation we get. Those angles also depend on the effective focal length of the lens and therefore, the deformation correction could be made dependent on module data or lens data.

If we now shot balls on a checkered background, we could make the balls look round again with volume deformation correction, but the checkers would get distorted instead. I might test this eventually.

Q1: Volume correction is independent of the lens correction module, and it only needs one piece of data: the focal length of the lens.
Q2: If I understand the question correctly, no, there are two different types of correction. The lens correction to eliminate the optical defects of this one, and the volume distortion correction to present an image more in line with what we are used to seeing. This only applies to photos taken at short focal lengths.