I am in an Intranet scenario with our WSS 3.0 installation. The user logged in
is the current Active Directory user of the machine. Assuming the user closes
the browser session, they are logged out. Signing on to another machine and
opening SharePoint in the browser then logs them in under their Active Directory
ID once again.

I don't understand what purpose you have for discovering this capability, though
as I said, I am a lowly WSS Intranet developer. Internet application may have a
different set of requirements....

We are getting lots of questions lately about being "Logged in" to SharePoint.
Please remember that SharePoint is a Web site, not a network file server.
Websites by definition are connectionless. That means that you are not logged
in to a Web site. You may have a session established on the web server that you
can re-activate if you return to get a new page, but its not a log  in. Your
login to the web server is maintained on the client in the browser, and not on
the server. Closing the browser will prevent you from reestablishing your
session state on the server when you return, but there is no way for the server
to tell your browser that it cannot reconnect. The best the server can do is
time out any active sessions. Those sessions are not tracked by userId, so you
can't destroy the session based on the user logging in from somewhere else.

In other words, you can't log the user off, because as far as the server is
concerned they were never really logged on. Its a web server not a file server.

You can change the inactivity timer to flush the session state after a period of
x minutes. But in most environments just refreshing the open browser on the
client will re-establish the session.