Although the hoi polloi (i.e., the masses) use the words Web and Internet interchangeably, there is a difference worth learning.
The Internet existed before the Web.
The first meaning of internet as it relates to computing was “a computer network consisting of or connecting a number of smaller networks, such as two or more local area networks connected by a shared communications protocol.”
The U.S. Defense Department had such a network called ARPANET–an acronym derived from Advanced Research Projects Agency Network.
From this DoD “internet” evolved “the Internet,” a global computer network that provides a variety of communication facilities–only one of which is the Web.
ARPANET was developed in the 1960s to enable researchers to use computers from remote locations. In 1982, the Internet Protocol Suite (IPS) was standardized and the Internet was officially defined as a global interconnected network. Although global, the new Internet was still mainly the reserve of people with the specialized skills needed to access it.
All that changed in the early 1990s when Tim Berners-Lee, a graduate of Oxford University, created a system of interlinked documents (e.g., web pages) that could be easily accessed by anyone using a browser. He called it the World Wide Web.
The Web, therefore, is not the Internet. The Web is one of many services that run on top of the Internet infrastructure. Other such services include email, FTP, and VOIP (e.g., Skype).
Here’s a typical misuse of the term Internet:
Are you unfamiliar with the Internet? If you want to know how to search the Internet, then you have to find the right search engine, type in your search as accurately as possible, and browse through the results to find the one you want. –WikiHow
I’m guessing that the Defense Department may know how to search the Internet, but when ordinary mortals go online to find cute kitten photos, they use search engines to search the Web.