I believe this is a new system. It's called two-factor authentication as opposed to two-step verification. To quote the FAQ:
> Is this different than Apple’s current two-step verification feature?
> Yes. Two-factor authentication is a new service built directly into iOS 9 and OS X El Capitan. It uses different methods to trust devices and deliver verification codes, and offers a more streamlined user experience. The current two-step verification feature will continue to work separately for users who are already enrolled.
Since I was already using two-step verification, I had to turn it off for the new, two-factor authentication, option to appear. I turned it on and it looks like it's working now.
I have to agree that this was very confusing.
EDIT: looks like I can authenticate from OS X now, nice. Before I had to always unlock my phone.
Thank you for this clarification. I just recently noticed and enabled two step authentication, and would have assumed I was already using the new auth without your post.
> Is this different than Apple’s current two-step verification feature?
> Yes. Two-factor authentication is a new service built directly into iOS 9 and OS X El Capitan. It uses different methods to trust devices and deliver verification codes, and offers a more streamlined user experience. The current two-step verification feature will continue to work separately for users who are already enrolled.
Since I was already using two-step verification, I had to turn it off for the new, two-factor authentication, option to appear. I turned it on and it looks like it's working now.
I have to agree that this was very confusing.
EDIT: looks like I can authenticate from OS X now, nice. Before I had to always unlock my phone.