How is this different from Google Authentication for Web Applications?

I suppose better late than never.

The modules do entirely different things.

This module implements the Client Login authentication method. In addition it implements a wrapper for the Google Provisioning API (which the other modules don't) and until recently Client Login was only authentication method that could be used with the provisioning api.

The Google Authentication for Web Applications implements the AuthSub authentication method. It's not clear if that authentication method can be used with the provisioning api.

The Google Authentication implements the OAuth authentication method and as of recently, you can use the provisioning api with it - though this module doesn't support it yet. I imagine we'll make the auth method pluggable in future versions.

You should read this blog post on the different authentication options offered by Google: http://stellapower.net/blog/google-authentication-methods