Totally fair! Frankly, I only know the distinction from a high school computers teacher who was adamant about the distinction.

I guess the easiest way to get the name is to see the “Web” as a “web” of hyper text documents, where hyperlinks act as the strands in the web (graph edges, if you will).

Honestly, like you say, it’s all built on top of a computer network (yet another web/graph). As a consequence, the distinction never really made a ton of sense to me, either.

Alas, this is the common parlance, so it is what it is.