What is the difference between share-on-Facebook and Facebook-like? I see both of them in many pages. Which one to use? What are the factor for choosing?
Sharing something on Facebook from a separate website will allow you to add a comment before it posts anything to your newsfeed. It will also show a small preview of the page you shared on your friends' newsfeeds.
Liking something from a website does not allow you to make any comment on it as you share it, and it only shows up in your friends' newsfeeds as " likes X"
Here is a good comparison of the two