OK, so I take it this is "anonymous" only for the application owner, Facebook still knows exactly where you log in, when and whatnot. So, and please correct me

OK, so I take it this is "anonymous" only for the application owner, Facebook still knows exactly where you log in, when and whatnot. So, and please correct me if I'm wrong, this is just logging in using Facebook without (probably) sharing "any" data with the software provider, right?