Adds label and comma-separated terms list to [downloads] shortcode based on taxonomy
<?php
/**
* Plugin Name: Easy Digital Downloads - Add terms to downloads shortcode
* Author: Easy Digital Downloads
* Author URI: https://easydigitaldownloads.com
* Description: Adds label and comma-separated terms list to [downloads] shortcode based on taxonomy
* Version: 1.0
*/

function sd_edd_downloads_shortcode_display_terms() {

    // use "download_category" for categories and "download_tag" for tags
    the_terms( $post->ID, 'download_category', '<span class="download-terms-label">Categories:</span> ', ', ', '' );
}
add_action( 'edd_download_after', 'sd_edd_downloads_shortcode_display_terms' );
To implement this snippet on your site, create a brand new, empty WordPress plugin and paste the above code inside.