There are 2 basic types of facebook like button:
1. The like button that appears on each blog post or website page using plugins such as the WordPress Social Share Buttons Plugin.
2. The like button that appears in the facebook likebox like you see on the WordPress Social Network Tabs Plugin.
When you like a blog post or article using a social share button this is basically just a way for you to let the authors know that you found that particular piece of content useful or interesting. These likes are based on the specific page URL and each page will have its own independent button.
On the other hand, when you like a facebook page such as http://www.facebook.com/DesignChemical via a facebook likebox you are connecting to that page. The page will appear in your facebook profile and your profile will also appear in the facebook page as someone who likes the page. In addition the Page will also be able to post content that you may find useful into your news feeds.