AOL was its own independent proprietary network, closer to a very large BBS, with email, chat, and content standards. It bridged to the Internet, as many networks at the time did (and many others did not).
The World Wide Web is a specific set of protocols (mostly: HTML and HTTPS, most would now include CSS and JS a well as other stsndards), which can run across the Internet or other networks, e.g., a disconected LAN.
AOL's joining the Internet had the largest immediate impact on Usenet, another protocol facility which can oerate over the Internet, but also transacted over phone lines (via UUCP) and avian carriers --- 747s carrying tapes between the US and Australia.
John Waterman's The Matrix (1990) is an excellent overview of early networking systems. That edition (there were several revisions) predates even the Web.