There's a lot of terms being tossed around in this thread that are inaccurate or misleading.
There is no such animal as an "electronic transfer". A transfer is an action, performed in person.....its not a form. It's where after the buyer/transferee has completed his 4473, the dealer has performed the requirements of the Brady Law, the dealer hands the firearm to the buyer.
eForm 4473 is form filling software download that ATF makes available for FFL's. It resides on the dealers computer and has no "connectivity" with the ATF/FBI/CIA/Trilateral Commission, etc. It allows the buyer transferee to use a tablet/phone/desktop or laptop to complete and sign the form.
There is no single "electronic system" either........there are several and none are operated by the ATF or FBI.
Some gun stores buy third party software that may integrate form filling software that mimics the ATF eForm 4473 and also updates the dealer bound book (Record of Acquisitions & Disposition) at the same time. Depending on the software vendor it may automate several functions including performing an FBI NICS background check.....so it would transmit certain information to the FBI. Some of these software programs may also connect with state POC's in those states where dealers do not contact the FBI for a background check.
The only information transmitted to the FBI for a background check is the buyer/transferees descriptive information: name, state of residence, place of birth, height, weight, sex, birth date, social security number, UPIN, ethnicity, race, if an alien their # and country of citizenship. The only information given to the FBI regarding the firearm is the type: Handgun, Long Gun or Other firearm. The FBI doesn't get the buyers address, doesn't get told whether the handgun is a pistol or revolver or whether the long gun is a rifle or shotgun and doesn't get any serial#, model name or even the caliber.