For a full list of calls available, see the API Reference page.
The session based authentication uses a session key instead of a token. It is mostly used with the Unity3d and Flash interfaces.
The Game API provides application level features like achievements on top of the session based auth. It is based on the open source Playtomic API but is not directly compatible.
The Game Analytics API gives application developers insights into how their game is being distributed and used by end users.
Used in mobile games to promote the network of mobile games.