Server Name or Instance Name?

Hello:

I had always heard that, when you move GP databases from one SQL server to another server that has a different name, GP user passwords will need to change.

First, on the "name", is it that the new server's name is different or that the SQL instance name is different?

I ask because, recently, we moved GP databases to a new server.  But, the full SQL instance "name" (the SQL server name before and the SQL instance name after the "\" character) are the same on both the old and new servers.

Too, the new SQL server is on a different domain, even though the SQL server name before the "\" character references the name of our previous domain.

And, I did end up having to change the GP user passwords.

It's no "big deal" or emergency.  I'm just curious, on all of this.

Thanks!

John