The menu admin doesn't have a way to switch the display of a whole menu according to group, but you can indicate visibility of individual menu items. This way you can use one menu but have extra items for members of admin or other groups. See doc.tw.o/menus, if you haven't already.
Another possibility is to use a module to display the menu. The menu tag is used as the module data. The module would be configured to display to admin only.