As a sibling commenter said, these days most people don't even really refer to the internet often, because it just is, ubiquitous, ever-present, and accessed via apps that abstract it out even more. Being connected is the default state of matters, and does not require a specific term. Just like you don't often need to refer to or think about the air surrounding you.
I worked as a consultant connecting businesses to the Internet, and boss asked me if I thought this WWW thing was here to stay, or a fad. I replied, "meh, it's a fad" because I had been underwhelmed by its implementation, compared to some mind-blowing infrastructure systems, GUIs and wonders like the MBONE (talk about fads).
I believe that the tipping point for WWW is when it was realized as a platform for delivering applications (SaaS). Once that angle became apparent, all resources were expended on making that a reality.