Something is a _secret_ only if at least two people know it. This makes a tremendous difference because now either of them might betray the confidence, a _private_ fact can't be given away by anybody else, it is yours to keep private or not.
Society blurs this line a lot by telling people things are "Private" when in fact they're only a secret, and then there is an opportunity to betray them. This happens for payment cards for example, bank representatives have been known to tell even a court of law that bank employees can't find out your PIN, so if a PIN was used it proves the customer was negligent or actively participated in the transaction. In fact, of course, the PIN is a secret, so the bank and thus its employees are aware of the customer's PIN and an insider could in fact perform transactions using PIN verification despite no negligence by the customer.
Society blurs this line a lot by telling people things are "Private" when in fact they're only a secret, and then there is an opportunity to betray them. This happens for payment cards for example, bank representatives have been known to tell even a court of law that bank employees can't find out your PIN, so if a PIN was used it proves the customer was negligent or actively participated in the transaction. In fact, of course, the PIN is a secret, so the bank and thus its employees are aware of the customer's PIN and an insider could in fact perform transactions using PIN verification despite no negligence by the customer.