I doubt the William units are West units. I live on the eastern side of the city and William units are here several times a night. I can tell you the the first number in the callsign is the shift 1=morning, 2=afternoon, 3=night. After the designator, the last number is the specific unit number. Just from listening, sounds as if the higher the number, the farther east their primary patrol area.
From what I've been able to tell, William units are "watch" units, Nora units are "traffic" and X-ray's are the semi-unmarked units. Occasionally you'll hear a "Sam" unit, those are usually either investigative or admin vehicles.
Hope this answered something for you.
Tom