Notice that one of the tabs at the class website is "Calendar". This shows all the homework due dates and all the test windows for the entire semester. There's also a calendar within WebAssign, but that calendar shows only work that has already been assigned as of the date you're looking at the calendar. So the purpose of the calendar at the class website is to enable you to map out all the work for the entire semester.
In contrast, the website calendar shows the WINDOW for each test and the final exam, i.e. not just the last day for the test but the entire window. The purpose of this to enable to plan well ahead of time when you will show up to take each test. There's no registration process for taking tests, but the testing center makes it pretty easy to find a time that's not likely to be crowded. So planning your tests ahead of time is wise.