The "web" often incorrectly used interchangeable with the term "internet" is in fact just another amazing service that is available on the internet(which is the network upon which the Web exists). There are many services that are available on the internet, we use email, often via a web based email browser like gmail or yahoo or even our own private network mail client like the Microsoft outlook web client. It is easy to get confused and think that email is on or part of the web, but it is not. It is a service like the web that runs on the internet.
Read more about the history and origins of the web here on wikipedia: http://en.wikipedia.org/wiki/World_wide_web
It is very important to understand the terms associated with the web and the manner in which it is managed and controlled. The world wide consortium is the organization that was created to manage the web services, it is generally contracted to WC3 (http://www.w3.org/Consortium/)
WC3 is more of a community than a business. The aim is clearly stated as wanting to lead the web to its full potential.