World Wide Web (or WWW) is too long to say and "The Web" never really caught on, but the Internet is not quite accurate. It feels like we need a word to differentiate IP from HTTP. Though, since we haven't come up with one yet, I guess we will just have to live with the WWW being called the Internet.
What exactly is your requirement for ‘the web’ catching on?
It’s used very often on ycombinator in submission titles and comments. I see it used by millennials and gen z on Discord, though more commonly as an adjective, eg ‘oh is it just web or is there an app?’
Sometimes they drop ‘the’ and it becomes “hey i saw this on web.” Online Korean comics are usually just called webtoons instead of manhwa. It’s used on corporate sites, ads, hotel amenities descriptions and in references to ‘the dark web.’
"Web" absolutely caught on. Web browser, web site, web app, web designer, web developer, web cam, (we)blog, web comic, surfing the web. These are all words most people know and use.
>It feels like we need a word to differentiate IP from HTTP.
We really don't, because technical accuracy isn't relevant to the vast majority of people, who aren't discussing protocols to begin with.
And anyway,I think people stopped referring to "the internet" in general once it became ubiquitous enough that it became more useful to refer to specific sites instead, or genres of services like social media. I think the only time people use "the internet" anymore is in reference to their ISP, eg: "the internet" going down.
It has to do with what protocol they are using to communicate with the server/cloud/whatever. If they are using HTTP/S (hyper text transfer protocol) then it is web/www. Otherwise, it is some other protocol. For example, email (technically) uses SMTP (simple message transfer protocol).
However, all of these run on top of the Internet Protocol (IP). So, everything is internet, but not everything on the internet is http.
Apps are almost certainly using HTTP under the hood to communicate with their servers, so technically they are a part of the web, which is a part of the internet.