Edit: After TSA inspects your checked bag, they keep custody of it and see that it gets loaded on the plane. The bag itself gets a second, small sticker of the type you get on the back of your boarding pass (and you get its mate, on your boarding pass...)
The second sticker should tell baggage handlers and TSA at the destination airport to take that bag to the controlled TSA pick-up area, where you will need to show photo ID or claim ticket to retrieve it.
The bag should not end up on the normal carousel - though if it doesn't show at controlled pick-up in a timely manner, you might want to check the carousel. That is where mine turned up at ATL... The system did work properly at the SEA end.