By my count, 16 US jurisdictions and 5 Canadian ones require a, generally annual, "safety inspection" often indicated by a sticker on the windshield or a receipt (actual or electronic) that must be presented to renew registration. Hawaii puts its sticker on the rear bumper, which a lot of car guys object to.
Most other states, including California, say a cop can require a motorist to get a letter from a mechanic that the car is safe if he thinks a car looks unsafe. A few others require a one-time inspection if the car is coming in from out of state title.
The inspection covers a list of the things you would think. Tire tread, brakes, bulbs, horn. Varies from state to state.
There just is no evidence that such programs work. The number of equipment failure accidents is statistically the same.
In my state, it is a waste. The amount the state gets is trivial, and the amount the garage gets has not been changed in decades. It is $12.66 total, with the state getting $3 of that. The garage is put in the middle of having to lose customers by not offering the service, or losing money by doing so. And also of p***ing off customers if they actually flunk a car. And of fudging by not doing anything, since $9 is a rediculous amount to make for the work involved if you actually followed the book.
Several states have eliminated these program recently. It is better just to take the fee charged and add it to the registration.