Ahhh. I see the problem. A Like button is for a specific URL. The Like button you're using on your home page is for your home page (
www.barkleyandpaws.com). Your Facebook Page is at
www.facebook.com/barkleyandpaws.
Those are two separate pages, in Facebook's eyes, and each has their own unique Like count. While they are similar, that's just coincidence. There's no guarantee that the 122 that have Like'd your home page have also liked your FB Page.
You can update the Like button to use a URL of your Facebook Page, if you want. You can't have the Like button on your Facebook Page point to any other page on your site though.
Hope that explains,
Alex