As Su explained, the issue stems from a post by Nik Cubrilovic. Here's how the theory went:
When you log into Facebook, the sites sets some cookies in order to authenticate you on every page load. These cookies are obviously linked to your account.
The issue discovered by Cubrilovic was that when you log out of Facebook, although it deletes all authentication cookies, it didn't delete a particular cookie that was uniquely linked to your account. When you visited any Facebook page in the future, although you weren't logged in, Facebook could in theory know who you were (or rather, who was the last user to log on to Facebook using this computer and browser). Of course, this implies that anywhere the Facebook Like button was being used, Facebook could link the website you were visiting with your account.
Facebook has stated that these cookies were never used for tracking purposes. They have now fixed the issue so that no account-identifiable cookies are kept when you log out. Some other cookies still persist, which uniquely identify the browser you are using - they claim this is necessary for spam purposes.
As for your specific question, if I'm not mistaken Facebook Connect requires visiting the Facebook site directly, and once back on your site no further contact with Facebook is made, so this is a different issue to the Like button. Facebook almost certainly tracks which domains are being logged on to with Facebook Connect, but it isn't able to track exactly which pages are being viewed and when.