I think there's a confusion here between diffs and patches. I would call the thing you're describing a patch, not a diff, and then everything makes much more sense.
(This is not helped by the fact that diffs often come with a .patch file extension… or that the "patch" tool processes diffs…)
Or anyway the nomenclature really sucks in this field. I guess I have no clue whether I have a minority view here.
Yeah the nomenclature sucks.
When talking about the file, the two terms are often used interchangeably (and are usually a .diff or a .patch extension).
For fun, the GNU Patch manpage says:
"NAME: patch - apply a diff file to an original"
followed by:
"patch takes a patch file patchfile containing ..."
"patch tries to skip any leading garbage, apply the diff, and then ..."