I'm talking about focus shift in the sense that if you focus on a point wide open and then stop down, the point of focus at that point in the frame moves forwards or backwards.
Yes, there are two different, but related, kinds of issues. The one you describe, when leaving (manual) focus untouched, stopping down will move the plane of best focus. This has to do with the changed contribution of edge lens rays to the focused image. Another issue is that the AF mechanism may pick a different focus plane wide open, then stopping down to the actual working aperture will result in a different focus plane.
This is caused by a combination of issues, where the AF sensor also is affected by the focus it detects based on edge rays, which would be different from focus detected while physically being stopped down, or when contrast detection in the center would be used. Field curvature is part of these issues, and also the fact that phase detect AF uses edge rays to do it's depth detection (just like a range finder with two viewfinder images taken from a different angle that need to be aligned).
Cheers,
Bart