Hi,
A menu item adds a link to a menu area. That link goes to display in your case a categories listing, and products listing. So it has settings both to display categories and products.
If the current category doesn't have sub categories, then you only see products.
A module directly display its content in its position. And the "menu" option of the module is the "target" menu item which used when you click on a link of the module to display the products/categories of that element.
And yes, when you click on a category, be it in the menu item categories listing itself, or in a module pointing to that menu item, it overrides the category selected in the settings of the menu item.