A GAME ID is if you have created a GAME Account with us using the email address and password.
A Social Federated ID is when you have used a third party account to create/ log in to a GAME Account. For example, if you use your facebook account.
Which is the better one to use?
Either. We give you the choice so you can pick which ever works best for you. Some of our customers like to set up an account separately and/or use a different email address to that on their Federated ID and some customers like the ease of not having to remember another password and set of login credentials.