John,
a "stacked" shot is a shot of a dog that has been set up by its handler according to the Breed Standard to show off the dog's basic structure. Here is an example of a stacked shot.



Note that the dog (in this case Rowdy) is set up with his rear hocks perpendicular to the ground, his front legs directly under his shoulders and his topline level. That's how they're supposed to look .

A moving shot is usually a candid shot taken in the ring (sometimes out of the ring) that demonstrates how a dog trots when it is moved during showing. The objective is to capture the dog fully-articulated with one front leg and one rear leg fully extended and the opposite legs fully contracted under the dog. Here's a sample of a moving shot.



In order to capture a dog that is fully-articulated, they have to move properly and be structurally balanced front and rear. That's why judges move the dogs. Some dogs look great stacked but don't move well. Some dogs don't look great stacked out but move like water flows -- effortlessly. The great dogs are the ones that look great both standing still and moving.

Hope that answers your question.

Jim