Classic proofing refers to the (mainly European) custom of firing the gun with special high pressure ammunition to confirm its quality. Depending on the country, there were multiple such firings, from white barrel to assembled gun.
The US acceptance marks mean that the inspector used gauges to verify the dimensions, but did not conduct an overpressure test.
Normally, acceptance stamps were issued on final assembly, and often also after repairs.
I used to love being able to hit hard at 1000 yards. As I get older I find hitting a mini ram at 200 yards with the 22 oddly more satisfying.