nav is used for groups of internal links (a elements). Generally this means the links should travel to separate pages, or change content in the case of an AJAX page. Expect some sort of content change when clicking on a nav item.
menu is used for groups of controls (a, input, button). Generally this means the inputs should perform a function within the page. Expect some sort of javascript interaction when clicking on a menu item.
nav: the navigation for the site.
menu: the menu for a web application.