Get list of custom taxonomies of custom post type and list of the posts under them

functions.php

//Downloads custom post type
function add_downloads_posts() {
	register_post_type(
		'download',
		array(
			'labels'       => array(
				'name'               => 'Downloads',
				'singular_name'      => 'Downloads item',
				'add_new'            => 'Add new',
				'add_new_item'       => 'Add new',
				'edit'               => 'Edit',
				'edit_item'          => 'Edit',
				'new_item'           => 'Add new',
				'view'               => 'Edit',
				'view_item'          => 'Edit',
				'search_items'       => 'Search',
				'not_found'          => 'No downloads',
				'not_found_in_trash' => 'Trash is empty',
			),
			'public'       => true,
			'hierarchical' => true,
			'has_archive'  => true,
			'menu_icon'    => 'dashicons-download',
			'taxonomies'   => array( 'type' ),
			'supports'     => array(
				'title',
			),
			'can_export'   => true,
		)
	);
}

add_action( 'init', 'add_downloads_posts' );

//Add "type" taxonomy to downloads post type

function create_types_hierarchical_taxonomy() {

	$labels = array(
		'name' => 'Types',
		'singular_name' =>  'Type',
		'search_items' =>   'Search Types' ,
		'all_items' =>  'All Types' ,
		'parent_item' =>  'Parent Type' ,
		'parent_item_colon' =>  'Parent Type:' ,
		'edit_item' =>  'Edit Type' ,
		'update_item' =>  'Update Type' ,
		'add_new_item' =>  'Add New Type' ,
		'new_item_name' =>  'New Type Name' ,
		'menu_name' =>  'Types' ,
	);

	register_taxonomy('types',array('download'), array(
		'hierarchical' => true,
		'labels' => $labels,
		'show_ui' => true,
		'show_admin_column' => true,
		'query_var' => true,
		'rewrite' => array( 'slug' => 'type' ),
	));
}

add_action( 'init', 'create_types_hierarchical_taxonomy', 0 );

loop.php

<?php $terms = get_terms( 'types' ); ?>
		<?php
		$allcats              = get_terms( 'types' );

		foreach ( $allcats as $cat ) :

			$args = array(
				'tax_query' => array(
					array(
						'taxonomy' => 'types',
						'field'    => 'term_id',
						'terms'    => array( $cat->term_id )
					)
				)
			);
			$customInCatQuery = new WP_Query( $args );
			if ( $customInCatQuery->have_posts() ) : ?>
                <div class="column-22 downloads-column w-col w-col-4 w-col-medium-4">
                <h1 class="downloads-column_title"><?php echo $cat->name; ?></h1>

				<?php while ( $customInCatQuery->have_posts() ) : $customInCatQuery->the_post(); ?>

                    <a class="downloads-column_link" href="<?php the_permalink(); ?>"><?php the_title(); ?></a>

                    </div>
				<?php endwhile; endif;
			wp_reset_query(); endforeach; ?>