Get a list of Link Categories ONLY

The code snippet below will retrieve the link_categories:

$sql = "SELECT t.name FROM $wpdb->terms t, $wpdb->term_taxonomy tt
       WHERE t.term_id = tt.term_id
       AND tt.taxonomy = 'link_category'
       ORDER BY t.name";
$results = $wpdb->get_results($sql);
foreach ($results as $result) {
  echo "<br />$result->name";
}
echo '<br />';

Fantastic! Thanks so much!

You are welcome! Now, please use the dropdown at top right to mark this topic ‘Resolved’.

Or use get_terms() and set the taxonomy to link_category.
https://codex.www.ads-software.com/Function_Reference/get_terms

Set hide_empty to false to show empty link categories.