Private network programs provide anonymity from those outside the network, but not from those inside the network. These networks are basically as safe as the members invited into them. For more information about Private networks.
Friend-to-friend (F2F) network programs provide anonymity from those outside the network and also from all those inside the network except for your direct friends (those who invited you or those who you invided into the network). For more information about Friend-to-friend networks.
Anonymizing network layer is a network layer that applications can use to anonymously and securely send messages to each other. Possible uses include anonymous surfing, chatting, blogging and file transfers. A VPN anonymizes your internet activity using a paid service. A web proxy allows for anonymous web surfing.