This one (below) tells you if an outlet is wired properly.
The other one is useful for checking for voltage on a circuit, but not if the wiring is correct.
Not all inspectors actually inspect the wiring. Some times they just sign-off on it.
Either they know the electrician always does good work, of the inspector is lazy.
View attachment 3003434
Power Gear 3-Wire Receptacle Tester-50542 - The Home Depot
"Please note that this tester does not indicate ground quality or reversal of grounded and grounding conductors."
They do catch some bad wiring. And there are newer ones with better ground testing but they cost $10 more and still miss some bad wiring jobs. Trip to gig is probably more dangerous than the venue wiring, drive a car with a seat belt and air bag - and now collision avoidance. Then somebody does something really stupid.
Old community halls and houses of worship are the worst. Some volunteer does the electrical. Good-hearted but could be a problem.