Multiple Custom Post Type with different Taxonomies

Try this:

function post_type_categories() {
        $field_args = array(
            'labels' => array(
            'name'              => 'Categories', 'taxonomy general name',
            'singular_name'     => 'Category', 'taxonomy singular name',
            'search_items'      => 'Search categories',
            'all_items'         => 'All categories',
            'parent_item'       => 'Parent category',
            'parent_item_colon' => 'Parent category:',
            'edit_item'         => 'Edit category',
            'update_item'       => 'Edit category',
            'add_new_item'      => 'Add new category',
            'new_item_name'     => 'New category',
            'menu_name'         => 'Categories',
            ),
            'hierarchical' => true
        );
        register_taxonomy( 'post_type_categories', '{your_post_type_name}', $field_args );
    }