I keep something private = I do not want to give out that piece of information. It’s linked to the word “privacy”. e.g. “I don’t want to give the man my password, that is private” e.g. “I won’t ask her about her health problems, that is private” I keep something a secret = I am actively trying to hide something or stop somebody from knowing something. e.g. “I won’t tell her you broke her necklace, I will keep it a secret” e.g. “Nobody knows where I have hidden the money, it’s a secret”