Authentication and encryption are traditional areas of computer security. These kinds of methods help provide privacy by making sure no intruder breaks into a system to receive data. Encryption is also a common tool in computer security to additionally make sure no eavesdropper on communications receives data.
Privacy problems causing the largest commotion in the press these days are not related to intruders breaking in to computers or eavesdroppers grabbing communication packets. Public concerns over privacy relate to the volume of information captured and shared freely. Solutions to these kinds of problems require examining stored values and the direct and indirect inferences learned when the information is combined with other available data. These are data privacy problems.
Example. A profile of the subject is stored in the computer by way of a person or another computer that has been authenticated by login with password and is authorized to read/write data on the machine. The communication pipeline is encrypted to avoid eavesdropping. The process is reversed for reading the profile from the machine. All of these were computer security protections, but the content of the profile can re-identify individual, and that is a data privacy problem.