With respect to gun shows, Lautenberg's S.22 provides an example of how to lock down sales at guns shows ("If any part of a firearm transaction takes place at a gun show" and "exhibits, sells, offers for sale, transfers, or exchanges").
I suspect that "internet sales" will not be limited to interstate sales as they currently exist, but will encompass any sales involving advertisement or communication over the internet, and probably other forms of electronic communication.
To my understanding based on what I've read so far, this is exactly what they are doing. Private FTF transfers will need to go through an FFL for a NICS check if the sale occurs at a gun show or was advertised on the Internet. Gun show NICs checks would also get priority over other checks, and the sale will be able to proceed after a two day delay, instead of three days like the current system (it will go down to 24 hours after four years).