In editing, to construct a scene from different footage takes seamlessly is called to cut on motion because it is achieved by literally cutting during the movement and following with a matching take. On the other hand, to cut on action is to match the movement between two different scenes. Let’s say the say for example there suddenly is an explosion in the room and the actor has to escape stage right. The next shot needs to show the actor entering the scene from stage left for it to be seemless, so the “action” dictates the screen placement of characters and the edit will not be noticed.
I came across this video of extreme cutting on motion based on Jim Carrey footage that illustrates something that may be difficult to explain. Beautiful cutting here.
P.S. Switch headphones off for watching ;)