At this point, given all the apps, IoT devices, etc. I feel like people know that there is more to the internet than what they can get to in their web browser. Go back 10 years or so and the browser totally dominated (aside from email and gaming perhaps), leading to the lack of differentiation you are referring to.
On the other hand, these non-browser communications I'm referring to almost always use HTTP APIs (a.k.a. web services) these days, whereas in the past they would use raw sockets or whatever else, so you could argue that even these comprise the web.
On the other hand, these non-browser communications I'm referring to almost always use HTTP APIs (a.k.a. web services) these days, whereas in the past they would use raw sockets or whatever else, so you could argue that even these comprise the web.