Terminal root login just works while being logged in as admin

I'm assuming it is intended.

You could try:

su yourAdminAccount

Password: enter.your.admin.password

su -

Password: enter.root.password

Or

su yourAdminAccount -c su -

Password: enter.your.admin.password

Password: enter.root.password

NOTE: These days very few people give the root account a password, as it is a known account that is frequently probed from the internet to attempt to break into network connected Macs. Most people use sudo to get root privileges. Of course sudo is not going to work for non-admin accounts, because if they could sudo, then they would by definition "Be" and admin account now. But you could still use su to get to an admin account, and from there issue sudo to become root

su yourAdminAccount

Password: enter.your.admin.password

sudo su -

Password: enter.your.admin.password

The difference is that you never need to give 'root' a password, so it is impossible for someone to guess the password when making a network attack.

I normally run standard. When I need to use sudo, I enter su - xxxxx (where xxxxx is the name of the admin account I use to authenticate). I then give the password for the admin account when prompted, and again after entering a sudo command.

Is this intended?

from "man su"

...

PAM is used to set the policy su(1) will use. In particular, by default only users in the “admin” or “wheel” groups can switch to UID 0 (“root”).

...