Dan says I need the FB API which I looked at and it seemed confusing
Hi, in the first answer above I said: "you need to install the facebook open graph meta tags" - this is different from the API. You do not need to use the API for anything. OSE uses the API for their data.
More info on open graph tags here, on the like button page
Open graph tags are meta tags you insert into the of your website on every page, so that when someone uses your share/like buttons, it sends information about your website over to Facebook, thus "counting" it as a share.
Do I need to install or connect properly with the FB API or just expect a discrepancy between what my site shows and OSE reports?
To reiterate, the action you need to take is to add the open graph tags to the of your website. You are running on WordPress so I suggest looking for a plugin that will do this for you.
Hope that helps! I know, it was a little confusing when I first tried to wrap my head around it.
To quote from facebook:
"The Open Graph Protocol enables you to integrate your Web pages into the social graph. It is currently designed for Web pages representing profiles of real-world things — things like movies, sports teams, celebrities, and restaurants. Including Open Graph tags on your Web page, makes your page equivalent to a Facebook Page. This means when a user clicks a Like button on your page, a connection is made between your page and the user. Your page will appear in the "Likes and Interests" section of the user's profile"
-Dan