There are a lot of definitions that get thrown around about “the deep web” and “the dark web.” It is frustrating how people use the terms without a clue as to what they mean. The deep web and dark web are NOT synonyms!
Starting with defining "The Internet," think of all the wires and connections as a highway system. When I talk about the general term of the internet, I am speaking about the technologies that move packets of information along wires from one destination to another, specifically the family of protocols known as TCP/IP (transmission control protocol - internet protocol).
The "World Wide Web” represents the many destinations that are connected together using the public highway system of the internet. When I talk about the general term of the World Wide Web, I am speaking about the technologies that create websites and webservers such as HTTP (hypertext transfer protocol) and HTML (hypertext markup language).
Where it gets confusing is how you apply the usage of the terms. Sometimes when people say "the internet" they are not describing just the highway system, but they are using the term to represent all the websites in existence. Likewise, often when people say “The World Wide Web” they use it to mean all the websites in existence.