PHP Code to Display Term URL & Name of a Post Under a Custom Post Type

Use get_object_taxonomies to get all of the taxonomies registered to a particular post type.

Also, don’t use query_posts for secondary queries. or ever, actually. Use WP_Query.

$args = array(
    'posts_per_page' => 1,
    'post_type' => 'movies',
    'orderby' => 'post_date',
    'meta_key' => 'featured_movie',
    'meta_compare' => '=',
    'meta_value' => 1,
);
$movie = new WP_Query( $args );

if( $movie->have_posts() ){
    while( $movie->have_posts() ){
        $movie->the_post();

        // your post template tags
        the_title();
        the_post_thumbnail('full-thumbnail');

        // taxonomies/terms
        if( $taxonomies = get_object_taxonomies( 'movies' ) ){
            foreach( $taxonomies as $taxonomy ){
                if( $terms = get_the_terms( $post->ID , $taxonomy ) ){
                    foreach( $terms as $term ){
                        echo '<li><a href="' . get_term_link( $term ) . '">' . $term->name . '</a></li>';
                    }
                }
            }
        }
    }
    wp_reset_postdata();
}