OpenID 2.0 is deprecated. Don't use it.
The current OpenID authentication protocol = OpenID Connect.
In the not too distant future, no one will even remember that something called OpenID 2.0 existed.
Maybe OpenID Connect should be OpenID 3.0? I think the idea was to show alignment with Facebook Connect's design...but more open. Remember, at the time Facebook Connect provided some good data--it was a massive user acceptance test.
IMHO, the blame lies with the OIDF for not delivering this message. OpenID Connect has been final for 4+ years. What's taking so long? Maybe it's not in the interest of the OIDF's controlling board members to promote this distributed identity infrastructure? MSFT wants you to use Azure AD. Google wants you to use their IDP. Maybe they don't want to promote until they have product ready? Stay tuned... I think when it's in the interest of the current finanical backers of the OIDF to promote OpenID Connect, no one will remember that old OpenID 2.0 thing.
They are very different things.
Yea..many people only remember the failed OpenID 1 & 2 specs...so, out-of-the-box there is some developer fatigue associated with Connect. However, federation standards have proven to be pretty sticky--SAML was written 10+ years ago. Hopefully as Connect continues to be developed, marketed, and implemented by developers, it will over shadow previous unsuccessful versions of the protocol.