Quick answer
A Facebook page like means someone likes your page; a follower means they will see your posts in their feed. People who like a page usually follow it too, but followers can unfollow without unliking. On the new Pages experience, followers are the main public number, so most businesses should grow followers.
The difference
Likes show that people approve of your page. Followers decide who sees your posts. On classic pages both numbers appear. On new-style Pages, Facebook shows followers as the headline number and likes less prominently.
Which should you grow?
Look at your page: if it shows followers at the top, grow followers. If it still shows likes, grow likes. Either way, pair page growth with post likes and video views so your posts look active. Compare page likes and followers in PKR.
Questions
Can I convert likes to followers?
No. They are separate actions, but most people who like a page also follow it.
Do you need admin access to my page?
No. Only the public page link.