How to display hierarchical and non-hierarchical taxonomies?

At the beginning, get taxonomies registered for a given type of post with get_object_taxonomies(). Then check which ones are hierarchical, e.g. using is_taxonomy_hierarchical() conditional tag. The last step is to display the lists.

// current post ID
$post_id = get_the_ID();
// taxonomies registered for this type of posts
$taxonomies = get_object_taxonomies( get_post_type() );

$taxs_tree = [];   // hierarchical taxonomies
$taxs_flat = [];   // non-hierarchical taxonomies
foreach ( $taxonomies as $tax )
{
    if ( is_taxonomy_hierarchical( $tax ) )
        $taxs_tree[] = $tax;
    else
        $taxs_flat[] = $tax;
}

Get terms from each taxonomy and display them.

// get terms as links
$terms_flat = $terms_tree = [];
foreach ( $taxs_tree as $tax ) {
    $terms_tree[] = get_the_term_list( $post_id, $tax );
}
foreach ( $taxs_flat as $tax ) {
    $terms_flat[] = get_the_term_list( $post_id, $tax );
}

echo '<span id="one">';
foreach ( $terms_tree as $links ) {
   echo $links;
}
echo '</span>';

Or:

//
// terms assigned to post, ordered by name, from all hierarchical taxonomies
$args = [
   'taxonomy'   => $taxs_tree,   // here you can pass array of taxonomies
   'object_ids' => get_the_ID(), // get only terms assigned to this post (current post)
   //'orderby.  => 'name',       // default
];
$terms_tree = get_terms( $args ); // array of WP_term objects

//
// terms assigned to post, ordered by name, from all non-hierarchical taxonomies
$args['taxonomy'] = $taxs_flat;
$terms_flat = get_terms( $args ); // array of WP_term objects

//
// display 
echo '<span id="one">';
foreach ( $terms_tree as $term ) {
    $link = get_term_link( $term );
    if ( is_wp_error( $link ) ) {
        continue;
    }
    echo '<a href="' . esc_url( $link ) . '" rel="tag">' . $term->name . '</a> ';
}
echo '</span>';

// the same with $terms_flat

The second solution (with get_terms) sort terms from all hierarchical taxonomies by name, while the first one (with get_the_term_list) sort terms from each hierarchical taxonomy separately.

References:

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