Looks like you already have it figured out, but here's an answer anyway. You need the smog cert when you go to AAA or the DMV to do the title transfer on the vehicle. If you go without the smog cert, they will leave the transfer in suspense until you come back with the smog cert. The seller does not need to get it smogged, the buyer can get it smogged, but the seller is responsible for it passing. If the vehicle won't pass, the seller is responsible, the title can not be transfered, and the sale can be cancelled.
The buyer is free to handle the smog anyway they want, but they can go back to the seller if there is a problem. Some sellers just go ahead and get it smogged before they sell it to avoid any problems, and a smog cert to an individual is good for 90 days. Be sure to get the actual paperwork on the smog cert, and take it with you to do the title transfer. Even though the smog is logged electronically, sometimes the system messes up and there is not a record of the smog, so bring the physical proof.
Oh, and the smog does not need to be in the buyers name, it's just on the car. No need to present bill of sale to smog shop. The buyer can use a smog obtained by the seller before the sale.