This is the difference that I'm talking about. Maybe this can only be called "Depth Compression" or "Background Compression"...but to me, the relationship between the subject (the brick...or a Grebe...) and its background CHANGED...that is perspective, no? I guess one could say that only if the relative positions of elements change, do you have a change in perspective. I would be willing to agree with that, however I have a number of friends who are wedding photographers who use the term "perspective" to refer to both changes in relationship...both change in relative positions of near/far elements, as well as the change in blur and apparent depth between a subject and it's background. I'm willing to accept that the latter definition is not accepted. I can just call it background compression from now on.
That is just blur, not compression, not background compression, not a change in perspective. With a longer lens from the same place with the same aperture the background will blur more, simple as that.
Your friends terminology is also incorrect, perspective is only
about the relative sizes of the objects within the frame, and that is only
determined by the distance from those objects. The background is more blurred in my 200mm shot, but the fences and tree are the same size in relation to the woman. If you look at the branch going across the right hand edge of your images, the 400mm shot is much more blurred, but the branch is the same size and angle in the 100mm shot. The same elements are contained within both frames, the fov and angle of view are the same.