About Facebook Connect
Facebook Connect is a method of linking Facebook accounts with external websites. It actually does link the sites in that when someone logs into a Facebook Connect site with their Facebook credentials then they are also logged into Facebook. When logging out of that site they are also logging out of Facebook. Additionally, if a Facebook user logs into their account then they will be automatically logged into all the Facebook Connect sites they have authorised. This concept is important to understand.
There is lots of introductory and technical information in the Facebook Developers Wiki
Note: fabEE does work in this way but unlike some other Facebook Connect sites it does not use asynchronous Javascript to maintain the links between Facebook and the website. This does affect the way that this process works. You may refer to the additional information for details.