In Photoshop, if I make any change to an NEF/RAW photo. What is the best/correct way to save it?
I don't see an option to save it as an NEF file. I do see a photoshop RAW file, but when I save it as that I get a warning about all of the changes possibly not being viewable the next time I open it.
It is not the simplest answer, at least understanding is not.
There is more to it than just a copy.
You keep your original NEF file, forever. The Raw editor never modifies it. It is always the original NEF file.
You Save the .xmp file. You copy them both when you move it, or if you let ACR do the move, it knows this. The ACR edit changes go into the accompanying .xmp file, which is just the list of the changes you have made. And any access, those changes are applied to a RGB copy of your original NEF file, and that RGB file is output, to your monitor, or to a JPG file, whatever.
The xmp file just stays in the folder with the NEF file. This shows your previous changes when you open it again. The warning was that if you don't also move the xmp file, you lose your list of previous edits.
This concept of unmodified NEF file, and the change list in the .xmp file, is the heart of the lossless editing feature in Raw. It is sort of mandatory, since we have no tools to change a Raw file, but it is also one of the biggest features. Whenever you decide you want a different white balance or brighter tones or whatever, have at it, change away, since you NEVER are shifting tones back and forth (which would not be lossless). Instead you are simply replacing one of the entries in the change list, with absolutely zero effect on your data, until you output some expendable copy.
The basis of any subsequent change is the original NEF file and your xmp previous change list.