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 ..."