What is the difference between instrument privileges and instrument rating?
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.