COmments not appearing … should they?

Hello!
I love how easy this is to install. I have a question….

Check out this post.
http://islandjay.com/caribbean-food-recipes-sunny-jim-whites-coconut-cornbread/

After I made the post on my site, I put it on facebook.
https://www.facebook.com/IslandJay/posts/199793620144565

After I installed the app I noticed that the 4 comments on facebook did not translate over to my web site. I found this odd since FB is links to the site article and knows they are connected.

Do comments on FB & my site not co-mingle? If not, then (Respectfully), what is the advantage of using any facebook comment app vbs the regular wordpress comment system and a decent spam filter?

Thank you!
Jason

http://wordpress.org/extend/plugins/facebook-comments-plugin/