[natdempk]

The terminology you're looking for here regarding the differing logins for different organizations is Single Sign-On (SSO) Providers. There are a bunch of different methods of implementing SSO, and companies that offer this as a service. Using the two-step login allows Microsoft, Google, etc. to redirect users to authenticate with their associated SSO Provider based on their username, or in this case email address domain, so that this login can be shared across other services a company utilizes.

[DelaneyM]

SSO has nothing in particular to do with two-step login.

Two-step login is just a way of getting a branded experience in front of the user as soon as possible, nothing more. It is neither necessary nor indicative of SSO (which you have described correctly.)

[rblatz]

>Two-step login is just a way of getting a branded experience in front of the user as soon as possible, nothing more. It is neither necessary nor indicative of SSO (which you have described correctly.)

That might be part of it, but the real point is companies do not want others to MITM their user's passwords.

[teddyc]

The custom Microsoft login for the university example cited is an implementation of SSO