How does social authentication work? network on client sites through your server?

Question

User identification

Hello.
I'm trying purely for myself, for development and for the future to understand the mechanism of authentication through social networks. networks on customer sites.
The simplest example is the hypercomments widget for example.
In the same place, for example, you log in through VK and only then on any other sites where there are hypercomments you are already authorized ...
What technologies are used here?)
As far as I understand, the scheme is as follows:
1. The user chooses through which to log in, for example, through VK
2. Opens popup with an application request, after confirmation, token
3 is sent to the server. On the server, through the token, we get information about the user and save it to the database.
4. some magic happens here and you are authorized on all hypercomments
Who is not too lazy, can someone tell how it works?)
Thank you!

Answer 1

You understand correctly. But if the user has already allowed access to his account, then step 2 can be skipped.
And in point 4, not magic happens, but an asynchronous request from a site with hypercomments to the servers of the same VK