The short answer is that the privileges are what the rating confers, and there are ways to get those privileges other than having the rating.
A commercial pilot licensee in most jurisdictions that follow ICAO certification guidelines may fly small planes for hire, doing service as a courier, air taxi, crop duster, etc. These do not necessarily require flying in IMC or in Class A airspace, and so a CPL holder must also have a separate "instrument rating certification" in order to fly IFR.
ATPL licensees fly in Class A as a matter of course, and that also often requires ascending and descending through the cloud ceiling which is IMC by definition. Therefore, the requirements for an ATPL in ICAO-compliant jurisdictions inherently include those required for the "instrument rating" applied separately to lower certification levels (private/commercial), and the resulting license for an airline pilot confers the same "instrument privileges" that the rating would.
Thus the difference in terminology; an ATPL holder in another country has "instrument privileges" as a consequence of his basic license and so does not need a specific "instrument rating". The same is not true for CPLs and so the law specifically requires the instrument rating as a prereq for a foreign CPL seeking an FAA ATPL.