The answers to your questions are tied to an understanding of the lower limits of the test methods. You spoke of two different types of PSA tests, and the primary difference is the lower limits of the measurement capability.
Probably the most important thing to understand, first, is that there is no such thing as "zero" PSA. The standard PSA test has a lower measurement limit of 0.1 ng/mL. Anything less than that is not "zero"; rather, it is simply "undetectable." Neurovascular nerve bundles, for example, will produce a trace amount of PSA, but below the measurement threshold of the standard PSA test. If you read about guys joining the "zero club", this simply means they have PSA below the test measurement cabability...not really zero.
The ultrasensitive test goes roughly an order of magnitude lower, into the hundredths. This test is newer and more expensive. Some surgeons will prescribe the ultrasensitive tests after surgery, and particularly if they saw or have reason to believe there might be cancer left behind. There is no "right" or "wrong." If they do prescribe the ultrasensitive test, they are interested in getting a "track record" of PSA levels to see if it rises over time. If it does start moving in an upward trend, then the patient will be better prepared for planning SRT, salvage radiation therapy. Some surgery patients will have measurable levels of PSA on the ultrasensitive test; other patients will be below detectable levels.
There is no threshold set in concrete when all medical professionals agree that biochemical reoccurrence has taken place, but you are correct in understanding that the most commonly agreed level is 0.2ng/mL.
Does this information help?