When you are stopped for a traffic citation, you are run through a much more comprehensive system known as NCIC. This database is far more detailed than the NICS one. No one except an authorized Law Enforcement Officer may access this information, although you used to have to use a voice radio to access it through a dispatcher. Even an officer cannot just "run" license plates and DL numbers through NCIC anymore. The slang shorthand for a call-in request used to be, "run wants and warrants" which gives you an idea how much more detailed it is than NICS. Today most departments have laptops in units so verbal calls are not used.
NCIC has numerous different parts containing all sorts of information, such as stolen property, address history, aliases, etc. I may be incorrect here, but I believe this system is a required part of the CHL process. NCIC is run by the FBI. I have no idea if NICS is a separate database, or just a limited access NCIC check. Some geek may know, if such things matter.
There are (pretty sure they still exist) even more comprehensive restricted databases that are operated on a need-to-know only basis.
I don't remember the wording on the 4473, but I think it allows FFL's to opt out of NICS for licensed purchasers because they wouldn't have the license without an NCIC check.
Key thing to remember for us "codgers" is to get with an attorney and get advice on how to keep prying govt eyes out of your affairs. IN ANY EVENT, back on topic. Here we go with more political correct Tom foolery, "Let's stop all those massacres by those elderly Americans with Alzheimer's."
