The animation below, from H. Tasiri, http://www.astronomynotes.com/nakedeye/csphlt5.htm, shows how these different apparent motions come about. The little stick woman on the globe is shown at different latitudes, keeping always her perspective on things, so the globe and celestial sphere rotate under her feet. Below the picture of the globe and sphere are diagrams showing how the motions of the stars appear to her in the different positions. She starts at the north pole and ends up on the equator.