Thank you Sue.
Yes I agree with you that uses a database for ADFS config stuff and being Microsoft it is a SQL server database.
However, there are no visible shared files neither the usual Visual Studio bits that you would see in program features. So the DB engine may be embedded in ADFS. What is interesting is to know what the SQL server list in SSMS looks at to identify what your SQL Servers are.
Because this information is a bit misleading. In that, this SQL Server cannot be part of a DBA responsibility. I mean my colleagues when they rolled out ADFS didn't know this and neither did I.
I agree we can safely ignore it but I would like to know more about it.