The original Stark 9-66 just had test sockets for all the older tubes including 4,5,6,7 pin tubes, up to Octals, Loctals, 7 and 9 pin miniature type tubes; in other words, tubes that had been produced up to the early 50’s.
The 9-66A included an auxiliary panel (screwed into the test lead compartment) that had special purpose tube sockets for European and industrial tubes. These sockets were still limited to a maximum of 9 pins like the older set in the 9-66.
The 9-66AU was a later version upgrade that included most of the former tube sockets in the 9-66A, but also added the later version compactron types up to 12 pins. These tubes started to appear in the late 50’s and were used extensively in TVs to reduce tube numbers and production costs.
Note that all of the test settings were still the same as in the earlier models. Another way of saying that is that the 9-66AU was downward compatible. However, the 9-66 and 9-66A’s were not upward compatible with the 9-66AU since 12-14 position setting switches were needed to accommodate the newer compactron types that only the 9-66AU could handle.