Let me expand on the other posts and hopefully answer your questions. Let's start with a basic concept. The root user and
only the root user can install system software. When you install OS X, it is installed by the root user. The root account is then disabled (root becomes a non-login user) and the setup process creates the first user who is an administrator. An admin user would be nothing without a special file- /private/etc/sudoers. This file grants admin users the right to become the root user and use all the tools owned by root to administer the computer. Here's a few example in the Terminal application:
<code>
[g5:~] mark% sudo -s
Password:
[g5:~] root#
</code>
The prompt says I'm the root user. Let's confirm this.
<code>
[g5:~] root# id
uid=0(root) gid=0(wheel) groups=0(wheel), 1(daemon), 2(kmem), 3(sys), 4(tty), 5(operator), 20(staff), 31(guest), 80(admin)
[g5:~] root# exit
exit
</code>
Sure enough. I'm the root user. Here's another example:
<code>
[g5:~] mark% sudo id
uid=0(root) gid=0(wheel) groups=0(wheel), 1(daemon), 2(kmem), 3(sys), 4(tty), 5(operator), 20(staff), 31(guest), 80(admin)
</code>
Every time I add sudo to a command, I become the root user. Even though root is a non-login user an admin user can become root. Sudo can be expanded using <code>visudo</code> to modify /private/etc/sudoers where you could grant user other than admins to use certain tools within the operating system. I strongly recommend that you do not modify /private/etc/sudoers. Here's some light reading:
man sudo
man sudoers
man visudo
Where it is possible to have root priviledges in the shell environment, the GUI user interface limits this ability. An admin cannot "see" inside another user's folder with the Finder. You can set a special permission bit to run a GUI application as the root user- the SET UID bit. Running a GUI application with the SET UID bit set to root is a security risk and normally should not be done. There are a parts of of the operating system that do run with the SET UID bit set.
So, an admin user is almost the same as the root user. An admin user must authenticate before changing a file they do not own- in other words an admin must think "What am I doing?" Each has the same power.