It's semantic pedantry but it's still fact. Private information is your name, address, social security number, or whatever you don't want everyone to know. Secret information is a level higher than that. People will kill each other to protect secret information because the level of seriousness is higher.

Usually when you have networks of people in authority keeping secrets you have corruption of whatever that institution is. That is because you cannot vet anyone without a background check and you cannot trust anyone who has secrets. If a human being is in a position of authority then secrecy is risk.

While we don't need to know exactly what was transacted it's a good thing that we can see the movement of money. If a lot of people give money to a particular address that is something which should be known to anyone. We don't have to know who they all are to know that.

Personal information is your identity. Public information is a lot of people who use Bitcoins like to buy books. Private information is the particular books that you chose to buy. If you don't want the world to see what you chose to buy then you need pseudo-anonymity to mask your email address, personal information, etc. It is still important for a society to know that certain books are popular without knowing which individuals are buying the books.