My Classes will show only the classes with the star selected.
All Classes will show all the classes accessible to you.
In Hapara to only show the classes you want in the "My Classes" list, you can clean up your class list by clicking the star to deselect the class which removes it from your "My Classes" list and is still accessible in your "All Classes" list. At the quarter or semester, you will go to "All Classes" and star the classes you want to be in your "My Classes" list. Pic below showing star location.