The Like button lets a user share your content with friends on Facebook. When the user clicks the Like button on your site, a story appears in the user's friends' News Feed with a link back to your website.
The Like Box is a social plugin that enables Facebook Page owners to attract and gain Likes from their own website. The Like Box enables users to:
See how many users already like this Page, and which of their friends like it too
Read recent posts from the Page
Like the Page with one click, without needing to visit the Page