Where to see the result of hook_menu()
hook_menu() is the method used by modules to add their own menu items. Most of the menu items you see on Drupal are added by modules with that hook.
The user interface allows you to add extra menu items that are not added by modules.

If you are asking the difference between creating a module that adds menu items with hook_menu(), and adding menu items with the user interface, hook_menu() allows to do things that are not possible with the user interface. For example, the menu that is visible when you hover the gear icon visible for a block is created with menu items added with  hook_menu(). (It requires the Contextual links module, which is a Drupal core module.)



The tabs that you see, for example, on a node page, are created with hook_menu(), or hook_menu_alter(). You could not create them with the user interface.



What you can create with the user interface are links that go:


In a menu block

 
In the Menu links


In the Secondary links