Facebook Likes Question in Ahrefs.

This will probably sound like a stupid question, but does a facebook like from a fan page count torwards a like for the website the fanpage is representing? I have the website link on the fanpage, and I have around 1500 likes for the fan page, but in ahrefs, it's only saying I have 5 likes, and I'm not sure how it got like that?

Do I have to have the FB like icon on my site? Right now I currently don't.

No, likes for fanpages are different from likes for your webpage.

Your site has to be liked in facebook,and to achieve that,all you need to do is use fb ads and promote your site link in facebook

They are 2 different things as YoungGooner explained above