Anonymity is traceless and keeps the user faceless (without an identity).

Privacy allows the user to pick and choose what is being shared, but the user is not necessarily trying to be “faceless”. This gives the user the ability to own and control their data more and to even be given something in return for giving information about themselves that they might otherwise want to keep private. Think about this as being more transparent for users and application hosts. When using an app on your phone that is “free” through Google Play, you are trading so much data about yourself, most of which you are not even aware of. For example, you do not have privacy when constantly being monitored by Facebook.