We are using MOSS 2007.

I have a web application that I extended via Central Admin because we
have dual authentication providers, Forms Based Authentication and
Windows Authentication on our Intranet side. When I open the Windows
Authentication site in SharePoint Designer and make a change to the
CSS, it is not being reflected in the Forms Based Authentication site
and I can figure out why.

Do I need to update the CSS for both sites when I make a change?

I was under the impression that if I went into the "style library" via
SharePoint Designer which by the way I use the Windows Authentication
site for SharePoint Designer and update the CSS and check it in, that
my changes would appear on BOTH sites but they are not.

Can anyone shed some light on how I can update the CSS and have it
reflected in both sites?