Basically, Usenet is a global network, but doesn't use the WWW? What does it use then?
Usenet is a network of servers which spread messages (posts) in newsgroups. They connect to each other, and people connect to them, over the Internet using TCP/IP, and exchange messages using the NNTP protocol.
The World Wide Web is a series of standalone servers, which people also reach over the Internet using TCP/IP and retrieve web pages using the HTTP protocol.
But do not confuse the Web with the Internet. Webpages are but a small part of the Internet and many other programs used to connect to each other long before the first webpages were ever served. (For that see history of WWW.) The one you might be most familiar with is email, which is usually sent via TCP/IP over the internet using the SMTP protocol, but there are many more.
Also note that in the past, servers would exchange email and Usenet messages over phone lines using UUCP as the protocol – forming an informal UUCPNET – as Internet connections were rare and expensive for a long time.