The formal definition of “to move” is: “to change from one place or position to another” or “to set or keep in motion”.
This moving usually happens by their own volition, but things can be moved by others as a “patient”. It should be easy to know if something is moving and all animal intelligence is based on moving. Moving to find food, find partners, and avoid being preyed upon. To represent moving, you would want motor neurons to move certain aspects of the body and they would need to be attached to whatever the mind is processing. As an action vector, any motor neuron action would represent moving. As an observer, to recognize moving, the agent would need to see movement on their sensors such as eyes and touch. The sensory data would need to be transformed in some way that it would recognize the movement as the meaning “to move”. “To move” is a catch all for any movement, so we could at least hand program it to see any movement to act as a default catch all if any vision data comes in AND the agent is not moving. In future versions, you would want to detect movement by touch as well.
The formal definition of “to do” is: “to act, to perform, to execute”. When an agent does something, it is essentially the same as movement, but it is usually with some intent. The question “What is X (you, him, it, that, etc) doing?” is asked when one wants to know what some agent is performing. Doing is abstract in that its usually tied to motion, but doing can be anything like thinking, doing homework, talking, etc. Doing is often associated with mental activity and goals. They are doing something because they have a goal in mind. When one asks what someone is doing, there is usually an implicit ask about the intended goal. If X was exercising and Y asks Z what X is doing, Z could say X is moving , X is sweating , X is losing weight, X is exercising, etc. We usually want to know what the intended purpose of the action is so saying “X is moving” is not as useful as saying “X is exercising to lose weight”. So to be able to model understanding of other agents “doing”, the agent would need to understand “agency” and “theory of mind”.