Movement is term used in Physics to describe change in position of an object over time. The object could be animate or inanimate. We are aware that motion or movement is described in terms of displacement, distance, speed, velocity, acceleration and time.
Locomotion in biology pertains to movements of various organisms and their capability to propel themselves from one place to another. These movements include walking, running, jumping, crawling, climbing, swimming, flying, galloping, slithering etc.
Locomotion is also used for robots in connection with their movements.
Even though movement is a synonym of locomotion, in our scientific life we use the term movement in Physics and Locomotion in Biology and for robots which emulate movement as accepted in Biology.
As per above discussion - for "fan is moving", I will prefer to interpret as the word "movement".
However, nothing stops you to say locomotion of fan. I will understand with a smile.