Check the full tutorial here : https://cedricleruth.com/how-to-display-a-custom-menu-for-logged-in-or-admin-users-in-wordpress/

DisplayDifferentMenuIfUserIsLoggedIn_Wordpress.php

<?php
//Add the following in your custom plugin code
//Note: if you prefer to add it in the function.php remove the array : add_filter('wp_nav_menu_args', 'display_custom_menu');
add_filter('wp_nav_menu_args', array($this,'display_custom_menu'));

/**
 * Filter menu to display 
 * logged-in menu if user is logged in
 * logged-in-admin menu if user is logged in and is an Administrator
 * logged-out menu if visitor isn't logged in
 *
 */
public function display_custom_menu($args = '')
{
  //check if user is logged in
    if (is_user_logged_in()) {
        //check if logged in user have admin privileges
        if (current_user_can('manage_options')) {
            $args['menu'] = 'logged-in-admin';
        } else {
            $args['menu'] = 'logged-in';
        }
    } else {
        $args['menu'] = 'logged-out';
    }
    return $args;
}

//Note : Now you just have to create 3 menus named logged-in-admin / logged-in / logged-out