The first difference between the Internet and the Web is the chronology of their creation. The Internet grew gradually out of projects like ARPANET, which established a packet switching connection in 1969. The World Wide Web only dates back to 1991, when Tim Berners-Lee led the creation of the first Web page using HTML as well as HTTP.
The Internet was originally created to help share scarce computer resources by allowing remote time-sharing so more people could use the existing computers, thus furthering the development of the new field of computer science. In 1971, Ray Tomlinson created a functional email program that added a new aspect to the Internet and quickly became one of the primary ways people used it. Other innovations, such as newsgroups, Internet role-playing games, protocols to transfer files, etc., then followed.
The World Wide Web (WWW, or Web) can be viewed as another innovation on the Internet. The Web made it possible for people to access information on Web pages and navigate through them. They didn't need to request access to a machine’s directory or email for a file to be sent. They just needed to navigate to a domain to see what was there.
In the simplest terms, the Web is a part of the Internet.
The Web in World Wide Web is not referring to a web of connected computers, but a web of information connected by hyperlinks. The linked network of computers, the Internet, is the base upon which the Web has been built and we depend on the Internet to give us access to that Web and allow us to add to it. Without the Internet, there is no World Wide Web. That being said, the Web is the most popular part of the Internet, so its easy to see why the average person considers the terms to be synonymous.