When you have booked valet parking, then all you have to do is drive to the departures hall. Here you will hand in your keys and car to a parking provider staff member, who will park your car for you. The main advantage of valet parking is the time you save. On return to the airport you'll call the parking provider again as soon as you have landed and a staff member will return your car to the arrivals hall.
With shuttle parking, you drive directly to the parking. A complimentary shuttle bus will then take you to the airport. The benefit of this is that you can be certain that your car is safely parked. The shuttle bus will collect you from the airport on your return and drop you off at the parking.