Thank you for the suggestion.
I reviewed the rendering, and I was attempting to work with a Phase One (P45+) IIQ raw file, bringing it into ACR, editing the image, and then converting it into PS. So it was good to check the original file, because I normally convert these in Capture One. I'm using an old (legacy) Mac Pro with the High Sierra operating system.
Picking up this line of thought, I instead opened the IIQ raw file in CO, and then converted it to a TIFF, specifying Adobe RGB '98 as the working space. (I wonder if it's embedding the profile? Or not?) I then opened this converted TIFF in ACR, worked on the image, and opened it in PS. Same thing, very different image. In addition, I opened this same TIFF in Creative Suite IV ACR (Snow Leopard for this), did some editing, and then opened the edited image into PS. No problem, the images between ACR and PS were exactly the same.
I was working with another photographer many months ago, who was editing raw Nikon images using Lighroom. She experienced the same problem then that I'm describing in this thread; when she converted and opened these images into PS, they were quite different.