What is the difference between a shower mixer and a tap with a diverter?
The diverter is a valve that redirects the water flow and water pressure. This mechanism 'diverts' the water to different water outlets, per example: shower arm, bathtub spout, and of course, the showerhead.
While the shower mixer, that allows you to control the water temperature and also pressure.
A shower mixer with diverter is a combination of both features. You can also get a shower system with a diverter.