The Facebook ‘Like’ widget is not connected to your Facebook page.
It simply displays the number of ‘likes’ your website has received, not your Facebook page.
Each time someone clicks ‘like’ or adds a comment, they are sharing your webpage to their Facebook timeline, not yours.
They are essentially publicly liking your page and, if they choose, publicly writing about it so it will appear to their Facebook friends.
If you want your Facebook business page to be directly linked to, you'll need to add it to the relevant Widget: Facebook/Twitter/YouTube/Pinterest/Google+/Instagram Page Links
That way when someone clicks on that link, they will go to your Facebook page where they can Like, Share and Comment.
For more information please see 'How to link social media profiles to your website.'