As introduced in https://www.drupal.org/node/254940#theme-suggestions-for-menus., a user can use THEMENAME_menu_link__MENU_NAME() and THEMENAME_menu_tree__MENU_NAME() to override theme_menu_link() and theme_menu_tree() for specific menus. This isn't really documented anywhere on the API site but is in the handbook here
Document these abilities. I am not sure if it should be in menu_tree_output() or theme_menu_link() and theme_menu_tree() etc.
User interface changes