When the NICS check is made at the time of purchase, without the carry permit, the only thing sent to the FBI is if it's a handgun or rifle. There are no other items on the form that identify the firearm.
If the buyer has a carry permit that information is entered on the 4473 and a NICS check is not required, thus the only record of the transaction is the 4473 which is kept by the FFL for the next 20 years.
During my compliance audits the ATF will look at a sampling of the forms but do not make copies or take any from the premises.