In looking a the list of "mentions "vs. "links" counted by Google,
many "mentions" appear to be active links. What is the difference
between a mention and a link and how do they each affect page rank?

Hi, 

A mention is simply text writing out a URL, like this 
://www.google.com

Some browsers will take that text and "create" link functionality to
it, meaning if you click on that text, the browser will react to it as
if it were a true link, and take you to that page. But trust me, it's
not a link.

A link uses the HTML code tag <a> and has a href option inside the
tag. This is in the coding of the page.

Only true links using HTML <a> tags are used for PageRank, mentions
are not used at all from outside domain/pages.

You can read about PageRank at these links,   
  
Google Information for Webmasters  
://www.google.com/webmasters/4.html  
  
Add your URL to Google  
://www.google.com/addurl.html  
  
Google Information for Webmasters  
://www.google.com/webmasters/2.html  
  
Google Technology  
://www.google.com/technology/  
  
Google's PageRank and how to make the most of it  
http://webworkshop.net/pagerank.html  
 
Google Under the Scope
http://www.searchengineworld.com/spiders/google_faq.htm
 
PageRank: Bringing Order to the Web
http://hci.stanford.edu/~page/papers/pagerank/
 
  
Thanks, 

webadept-ga