Internet technically began to exist in the form
we know it on January 1, 1983 when its predecessor, Arpanet began
using TCP/IP – the system of network communication still used today.
The web was invented by Englishman Tim Berners-Lee in
1989. The World Wide Web is made up of servers (which serve the
pages) and clients (like Firefox, Safari, and IE) which display the
page.
The Internet is the set of technologies beneath the web which
enable the web to exist. If the Internet did not exist, the web would
not function. If the web did not exist, the Internet would still function.
Other programs that use the Internet and have nothing to do with the web are email, IRC (Internet Relay Chat), most
internet messaging programs, newsgroups, BitTorrent, telnet, FTP,
etc.