Robert_Charlton - 6:42 pm on Jul 28, 2008 (gmt 0)

If I'm understanding your question correctly (and I may not be), you're talking about two different uses that Google makes of the word "related."

I just noticed that my searches are coming up with links to related terms under the search results. Not all the listings had it, but it does have these same listings appearing at the top of the page.

Searches related to:, which appears at the top or bottom of some serps pages, is Google's attempt to help searchers find more precise results. These appear at the top or bottom of some serps pages, and are suggestions for more precise searches. They're most probably based on Google's historical data of query refinements that searchers have made.

Google Related Links under listing.... ...The related links for the site above ours are totally different, but definitely targeted to their topic.

I'm assuming you see these when click the "Similar pages" links underneath each result on a serps page. These links bring up the related:domain operator results for the domain displayed. The last time I checked carefully, the related:domain results were domains that shared common inbound linking sources with the domain queried.

Also see...

The Related Google Operator
[webmasterworld.com...]

The related:domain operator and Searches related to results are completely unrelated. ;)