The aircraft type certification uses the generic BAe146 designation; the Avro RJ is a subtype.
Re: INSPECTION SERVICE BULLETIN ISB.21-1156, this is titled “BAe 146 SERIES/AVRO 146 RJ SERIES AIRCRAFT” and therefore applies to all BAe 146 Series and Avro RJ aircraft.
Re: Airworthiness Directive 003-10-2002, this is titled as “Applicability British Aerospace BAe 146-100, -200 and -300 Series aircraft”, thus only applies to BAe146 aircraft.
The difference in the two documents in their applicability is probably that the service bulletin is published as a generic procedure that might be called-up either as a specific check or used in a scheduled maintenance program, and details how the check is to be carried out; whereas the AD specifically requires a check of all BAe146.
Incidents may have been identified in the BAe146 only, and if oil was found in the ducts and if it was judged that this might have contributed to air conditioning problems a mandated check is call for. The frequency of the check suggests the abjective was to avoid repeat incidents from any failure to clean out the ducts after an initial incident.
The mechanism of the check is maintenance good housekeeping, which IMHO suggests that some operators were not checking this area after reported oil leak events. It had also been reported elsewhere that many oil leaks originated from overfilled (over serviced) APUs, and thus the AD (CAA lacking hard evidence) took a side swipe at tardy operators to improve servicing standards and ensure that a good clean up of the Air Cond system was undertaken to prevent repeat occurrences.