Here’s a little tidbit I can NEVER find when I need it: If you need to get all the tags that belong to a current post, here’s the function:

$tags = get_the_tags($post_id);

This will return an associative array of tags, with all their relevant info.

BONUS
If you need the same thing with categories, here’s your function:

    $args['fields'] = 'all';
    $categories = wp_get_post_categories($post_id, $args);

Including the args bit allows you to retrieve all the category info. If you leave that out (and use only the $post_id argument), you’ll get an array of relevant category ids, but no other info.

Big thanks to Clay Lua at hungred.com and his post Get Tag with Post ID in Wordpress for pointing me in the right direction.