I would guess the non-www version is what you have in Dashboard > Settings > General, and then you likely have also some htaccess code redirecting the www version to the non-www version. To make your site use www, you would need to do some editing in your database and also reverse the redirect. I am not able to walk you through all of that, but here are some related info links:
https://www.google.com/search?q=wordpress+www+non-www
https://forum.ait-pro.com/forums/topic/htaccess-redirect-www-to-non-www-htaccess-redirect-non-www-to-www/
