I my opinion "Save a Copy" has the wrong name its name should be "Save a Version" I believe Adobe named it "Save a Copy" because of how Apple change their file system to version with a " copy" in the files name. Adobe could not change all OS version File system so they created Photoshop file versioning "Save a Version/Copy" and Change how Photoshop "Save As" Feature Works reverted to how Savs As work years ago where it could not save a flat image file format from a layered Document. However, for the users convenience Adobe added a Button into the changed Save As UI "Save a Version/Copy" Adobe added versioning to Photoshop for all OS version. Adobe did not add this to iPads Photoshop for it can not save files it uses cloud documents can not deals with files.
Since 22.4, if your file contains items that are not supported in your required format (e.g. layers or 16 bits/channel or hidden pixels etc) then the file format is moved from Save As (Shift+Ctrl+S) to the Save a Copy command (Alt+Ctrl+S). This was driven by changes in the Mac Operating System, although the changes are applied to both Mac and Windows versions to keep them aligned.
In the case of PDF it will appear in Save a Copy as the dialogues that follow the choice of the PDF format, allow elements of the file to be lost (e.g. downsampling or not keeping editability). So it is in the Save a Copy category.