GFCI Question

It seems to me that when a GFCI outlet seemingly “trips” when tested using it’s own button yet does not actually remove power, and will not trip at all using an external fault that it is indicative of “something” other than a bad GFCI in need of replacement. For the life of me I can not remember “what” if anything at all. Maybe i am just out in left field. What say you all.

Line/Load reversed is the simple answer. The more complicated one is:

Thank you so much! I had a feeling that was the indication but could not remember for sure. It’s hell getting old!