The English words motion and movement are similar. They both have to do with “changing position or going from one place to another.” (Collins English Dictionary)
Then what’s the difference? Here are a few ways of putting it:
motion is used to describe physical properties, while movement is used to describe the qualities of motion. Ref.
motion doesn’t always imply a purpose, and movement usually does. Ref.
The difference is very fine. I would say that movement is déplacement d’un lieu à un autre [displacement from one place to another] whereas motion is le fait de ne pas rester immobile [not to stand still]. But usage and context are crucial. Ref.
People may not be consistent about it but for the purposes here they can be distinguished. Motion is the general term in kinematics, the study of motion. It says nothing about the purpose of a motion, or its origin and destination. Something just happens to change place.
However, movement includes some purpose, some origin and destination. A movement is a complete motion, from beginning to end. So movement would be preferred in the arts and social sciences and motion in the natural sciences.
Physics studies motion. Transportation studies movement. They may both speak about something changing position but there is a different perspective.
A body has its motion and a movement has its figure. A body is flesh-and-blood 3D, with its motion only adding a 1D time parameter. A movement has 3D animation and life, with its stance only adding a 1D space parameter.