Currently, Azure Management Portal has two versions:
They are on two different domains (even different data centers, I guess) but sharing the same login session, i.e. once you logged in one of them, you can enter the other without any authentication.
Can anyone explain how it works on dotNET Stack?
Based on your description, I think what you are talking about is Single sign-on (SSO). SSO is a session/user authentication process that permits a user to enter one name and password in order to access multiple applications. The process authenticates the user for all the applications they have been given rights to and eliminates further prompts when they switch applications.
Can anyone explain how it works on dotNET Stack?
To implement SSO, you need to create a shared authentication server or use a exist shared authentication providers(ex Microsoft/Google). Here are some examples of implement SSO using ASP.NET.
Basics of Single Sign on (SSO)
Using OAuth Providers with ASP.NET MVC 4
Introducing Single Sign-on to an existing ASP.NET MVC application