You don’t have to confirm that the proper connector was used, but you want to be able to identify when a connector was used in a manner for which it was obviously not designed, or fastened with fasteners that are obviously incorrect for that application. 8d sinkers are always wrong. #8 nails are usually wrong, but both are common in some areas (S. CA for sure).
Different connectors are made from different gauge steel and designed for use with different types and numbers of fasteners. Few, if any of us, have all that memorized.
Typically, you’ll just be judging from the head of the fastener whether the correct one was used. The vast majority use #10 hanger nails until you start seeing heavier gauge connectors, usually hangers and straps, and then you’ll be looking for the heads of the larger fasteners you saw in Marcel’s chart.
There’s a lot of good information in those Simpson catalogues. If you have time to actually read through the general information and the fastening requirements for common connectors you can learn a lot in an hour!