Technically it is "Buyer background check."
In Louisiana, we have the paperwork called in and once approved, you walk out with the gun. Most often it takes a couple of minutes. However I have been delayed on a few occasions but was able to pick the gun up the next day with one exception. Once I was delayed and it took five days before I was cleared. It seems I was cleared late in the day of the purchase but nobody at the FBI bothered to call back with approval.
I envy those in states that allow the CCW to serve as an approval.