That is true. The World Wide Web is kind of the GUI for the internet, which had already existed for years before the WWW. The internet should be thought of as the infrastructure of sending data from node to node. Software applications are built on top of that layer. WWW and browsers simply use the infrastructure to display information graphically across the internet.
Email used the internet before the WWW, as well as file transfer protocols like FTP. There was a bulletin board application called Usenet, which had a lot of forums, some not unlike Free Republic.
I used Fidonet and IIRC several mail programs like PINE.