Try it. Setup different scenarios, publish, and see how browsers render it.
There are several reasons designers use both together, but the main reason is usually to stipulate a layout constraint.
If you have a DIV with width 300px, but the contents are 400px wide, the DIV will expand to fit those contents ( unless hidden or auto overflow is also set ). Max width acts as a maximum, so if you have max-width 350px, then the DIV will be 300px with contents that fit, and no larger than 350px when the contents are wider than 300px.
Designers often use different units as well, particularly on larger layouts, e.g. width 100%, but max-width 1800px. Keeps layouts from getting ridiculous when the content doesn’t scale.