wp custom nav. this is also outputting every menu item found in wp, and not only a specific custom menu 'test'. registering or not doesn't make a difference.

gistfile1.txt

<? php
$menu_name = 'test';

    if ( ( $locations = get_nav_menu_locations() ) && isset( $locations[ $menu_name ] ) ) {
	$menu = wp_get_nav_menu_object( $locations[ $menu_name ] );

	$menu_items = wp_get_nav_menu_items($menu->term_id);

	$menu_list = '<a>test</a><nav id="bt-menu" class="bt-menu"><ul id="menu-' . $menu_name . '">';

	foreach ( (array) $menu_items as $key => $menu_item ) {
	    $title = $menu_item->title;
	    $url = $menu_item->url;
	    $menu_list .= '<li><a href="' . $url . '">' . $title . '</a></li>';
	}
	$menu_list .= '</ul></nav>';
    } else {
	$menu_list = '<ul><li>Menu "' . $menu_name . '" not defined.</li></ul>';
    }

$defaults = array(
	'theme_location'  => 'codrops',
	'items_wrap'      => '<ul id="%1$s" class="%2$s">%3$s</ul>',
	'depth'           => 0,
);

wp_nav_menu( $defaults );
 ?>