Similarities between Facebook and LinkedIn are the messaging aspects, the "friend" suggestions, and the profile information you set up on yourself.
Differences between Facebook and LinkedIn are that LinkedIn is professional and you would never want to put anything on there that is not considered professional. Where Facebook is more of a social site. You can put pictures from your vacation, baby shower, or sisters birthday up.
Both LinkedIn and Facebook have the purpose of connecting you with people you might not have otherwise been able to connect with but the reasons why you connect with them are different.