Ah, ok. I think I just had a moment of clarity here.
The Category List links to category pages. What I mean by this is that each link is intended to take you to a page that will show you all entries in that category.
Whereas the related category mode is intended for use on a “single-entry page” wherein it is for display of a single entry (as opposed to multiple entries within that category). The category list tag will not take you to a single entry page.
Essentially, you’re getting results we’d expect from ExpressionEngine, but not the results that you need.
Make sense so far?
So, we need to figure out what you need in ExpressionEngine terms. Right now, from what I understand, you want to show a single entry (noted by the URL title in the third segment). Under that single entry, you want to show a list of other entries that share a category from the primary single entry. Correct?
{exp:weblog:entries weblog="expect" orderby="date" sort="asc" limit="1" show_future_entries="yes"}
{title}
{body}
{/exp:weblog:entries}
{exp:weblog:entries related_categories_mode="on" orderby="date" sort="asc" weblog="expect"}
<a href="http://{title_permalink=site/expect}">{title}</a>
{/exp:weblog:entries}
What you’ve got here will do that if the URL title is in segment 3:
ie: http://pamfanjoy.com/index.php/site/expect/pam_fanjoy_as_child_specialist/
But, I think where we are all getting hung up on is how you wish to navigate to that page. Can you tell me how you want the navigation to appear? I think we need to step back and know what your output goal is before we confuse ourselves even more.