is ‘www’ a normal sub-domain? Yes, it is. From the point of view of DNSs it is a totally normal subdomain.
is some special kind of sub-domain? Yes, it is, indeed. It is so commonly used that most Registrars and Hosting providers do automatically create it for you and permanently redirect it to the web server hosted with them.
in your case, it seems that this is not what happens. So, create it and permanently redirect it, instead of creating a new index page for it.