Google+ Sign-In is an implementation of OpenID Connect, with some nice features built on top:

"Google+ Sign-In is built on the OAuth 2.0 and OpenID Connect protocols. It supports over-the-air installs, social features, and a sign-in widget on top of standardized OpenID Connect sign-in flows. Google+ Sign-In works for all users with a Google account, whether or not they have upgraded to Google+." [0]

I don't understand where all your other conclusions came from.

[0]: https://developers.google.com/accounts/docs/OAuth2LoginV1