What do you mean by private?
In my state if you purchase from a gunshop, which I have done once for my son’s hunting gun, one has to fill in state paperwork which is supposed to be destroyed after a background check.
Recently I read, here on FR that there are states who are actually keeping the supposedly destroyed information. I would not put it past the leftists running the government in my state.
Private sales are not governed by state guidelines.
Private seller {you} sells to private buyer {me}. This is the preferred way to conduct firearms transactions. {assuming you know I'm not a criminal} No info enters the database for future registration/confiscation.