As I see it, 'private' means that only the addressee should open it.
(i.e. it's not to be read by anyone else who shares an office, or in-tray, with the addressee).
But that, on it's own, doesn't mean that the addressee can't then divulge the contents to certain other people. So a letter marked 'Private', sent to 'The Head of Personnel' should only be opened by him/her. However adding 'confidential' means that he/she should not then discuss the contents of the letter with (say) the head of another department within the company.
However, in reality. the words 'private' and 'confidential' just get thrown together out of habit, without the person writing them really thinking about what they actually mean.
There's an analogy with 'terms and conditions'. I'd be prepared to bet that most people who provide a list of "terms and conditions" wouldn't know which of their numbered items is a 'term' and which is a 'condition' ;-)
Chris