Am I right in thinking the difference between using Soft Proofing to a different colour profile (in Photoshop for example) and just changing the colour profile is that with Soft Proofing use of the Relative/Perceptual options (in Photoshop) actually modifies the values of the pixels before changing profile so when the profile is changed more of the pixels are properly mapped to the new colour model.
Usually not, although I guess it could be done that way. Normally though, pixels are passed though a color transformation on the display path. Some software use a full color matrix but most and certainly hardware based solutions use a 3D LUT (Look-Up-Table) for efficiency.
This means that the same pixel values remain in the image but go through the LUT which sends different values to the display. The 3D LUT does not cover every possible point in the input space so we usually interpolate in-between.