Im little confused about the difference between "SP State Service Application" and "SP Session State Service", while i know that session state service is used for storing sessions in SharePoint.
In SharePoint the State Service Application is a shared service that is used by the internal office elements like Info Path forms , Workflow forms to store the temporary data in SQL Database.
This Service is Automatically installed as part of the SharePoint installation.
and in order to use the Session state in SharePoint the Session State Service Application need to be configured in SharePoint so that we can maintain the temporary values in the session using the variables in our custom web parts or App parts.
In SharePoint by default the session state is disabled , it needs some configurations to enable it.
SharePoint uses ASP.Net for session management.
Please refer these articles for more info :