They have multiple web servers so they called them www1, www2, etc because you can't set up multiple web servers on the same domain name and name them all www because then there would be no way to tell which server to access.
Are you saying "www1" is to www1.example.com as "mail" is to mail.google.com? Does this mean that "www" a subdomain but many modern web servers are able to assume a subdomain of "www" when none is given? (because "www.mail.google.com" doesn't give a response)
With subdomains you could pritty much have anything you want. www. is not required for nearly all web browsers and you can do quide a few subdomains (If your hosting provider allows it)
gives the same result as www.google.com
but there may be a backup server running on www1.google.com
incase the main server goes down
its sort of like server 1, server 2 etc.
You could have a subdomain like www.bob.homer.boris.yourdomain.com
and send it to a different server to yourdomain.com