Nav menus all outputting the same links

I have registered the following menus in my functions.php

Note that register_nav_menus() which uses register_nav_menu() (note the singular “menu”) does not register or create a navigation menu; it only registers navigation menu locations which you can assign one or more (navigation) menus to, and for displaying the menus assigned to a specific location, you can use wp_nav_menu() just as you’ve already tried.

How do I get menus 01 and 02 to show their own links?

The problem in your wp_nav_menu() call is because you’re not specifying the proper navigation menu location which is identified by the theme_location parameter like so:

<?php wp_nav_menu( 'theme_location=footer-01' ); ?>
<?php wp_nav_menu( 'theme_location=footer-02' ); ?>
<?php wp_nav_menu( 'theme_location=footer-04' ); ?>

More details based on the wp_nav_menu()‘s reference:

Usage

wp_nav_menu( $args );

Given a theme_location parameter, the function displays the menu assigned to that location. If no such location exists or no menu is
assigned to it, the parameter fallback_cb will determine what is
displayed.

If not given a theme_location parameter, the function displays

• the menu matching the ID, slug, or name given by the menu parameter; e.g. wp_nav_menu( 'menu=123' ) or wp_nav_menu( [ 'menu' => 'My Menu' ] )

• otherwise, the first non-empty menu;

• otherwise (or if the menu given by menu is empty), output of the function given by the fallback_cb parameter
  (wp_page_menu(),
  by default);

• otherwise, nothing.

(Note: I slightly modified the above quote.)

So be sure to check the reference/docs and supply the proper function arguments. And remember that the above $args can be an array like array( 'key' => 'value' ) (or [ 'key' => 'value' ]) or a query string like key=value&key2=value+2. Both will work in most cases, but when the value contains a space or the value is complex (e.g. it contains HTML tags), then you should use the array format. 🙂