actually both these domains are different. since the backlinks were built with the www one, therefore, no backlinks are shown for the non www version
If you're using this link http://www.abc.com to create backlinks then all your links would be see in this url http://www.abc.com
With and without the www are seen as separate sites. That is why the search engines show pages and links to both urls. To fix this problem, edit the htaaccess file and set up a 301 redirect that points http to www. Or if you want it the other way, make the 301 redirect point www to http. Whats going to happen, people will post links to your site in both versions, and you page rank is going to be split. Its best to use the htaaccess file to rewrite the url so that one or the other can not be accessed.