who keeps the current tag

YOU keep the old tags. You're not supposed to let the new owner drive off with them. If you do let them drive off on your old tags, you might find yourself responsible for a lot of driving offenses you weren't behind the wheel for. After the new owner receives the title or certificate of title from you, they use that to obtain a temp tag that they can then use to drive your car off with. Again, you keep your old tag. Registration stickers you can scrape off. Most states title web sites have a statement saying you are required to inform them when you sell, donate, or trade your car.