Moving Lights are not stationary. That may seem ridiculously simple but that is the essence of their functionality. They are not stuck doing one thing. They can do many things and then change and do those things differently. If you consider many of the properties of light, Intensity, color, location, sharpness, texture, movement and so on, the moving light can do all of those things and change each one of those properties.
General types of "Movers"
Some other important things to note about "Movers"