Read these pages if you haven’t already found them.
Template Changes – https://lorelle.wordpress.com/2007/01/26/wordpress-21-template-tag-and-function-changes/
codex for list categories – https://codex.www.ads-software.com/Template_Tags/wp_list_categories (mentioned in post above) and
codex for bookmarks – https://codex.www.ads-software.com/Template_Tags/wp_list_bookmarks
Southwest, if you’re still looking – Try replacing <?php get_links_list(); ?>
with <?php wp_list_bookmarks('category='); ?>
Here is what I have done on talkjunkie.com to separate and call the categories and the link(bookmark) categories: On the left sidebar I’m using – <?php wp_list_categories('orderby=name& hide_empty=0&exclude=34,29,36,31,33,30,37,32,35& hierarchical=1& title_li=0'); ?></ul>
On the right sidebar I use – <?php wp_list_bookmarks('category=33,34,37,35'); ?>
<?php wp_list_bookmarks('category=30,31,32,36'); ?>
If anyone comes across a good explanation of why the category merge is an improvement, I’d love to read it.