Internet=global computer network. Web=interlinked hypertext documents accessed via Internet, also it's a gui for stupid people, that's why your grandma can use it.
All tor and other programs do is offer a way to transfer information over the Internet, but not necessarily using the Web. Kinda like IRC back in the day. Or a listserv, or e-mail not based on a Web platform.
Surprised people are shocked by this. Did you think terrorists and pedos were just creating public Websites?