One path alias for differents / multiple internal path?
You cannot have one alias for two items. That's not how router works. On the other side, you can create a page only guests will have permission to see, and place it under the same name in the same menu. Then both guests and logged in users will see identical menu, but they will actually get different set of menu items.

If that's not enough, you can use Menu per Role to get more control of who sees what in your menus.