A licence is a licence with its own specific privileges and a Class rating is a rating to fly a particular class of aeroplane regardless of what licence privileges you are exercising.
Any Examiner qualified to examine for that Class rating can conduct a revalidation by test, in any aircraft within that Class. The format of the test can be found on the Examiner Record sheet
SRG1157
They put your number onto the Revalidation page so that it cannot be transferred to someone else. Your FRTOL should say RT plus your ref No