Jeremy Keith attempts to make this distinction, using Angular and the concept of “enterprise” software as the catalyst.
“Of the web”: Built of fundamental principles of the web. Universal access.
“On the web”: The web as a delivery mechanism. The owners dictate use.
Jeremy, who has been banging the progressive enhancement drum since forever, is predictably an “of the web” kinda guy. He only takes issue with the fact that other folks might be forced into working against their principals because of an above-their-head software choice.
I’m slightly less concerned. It actually makes me feel better thinking of things in those terms. While I feel more aligned with the fundamental-principles thinking, I’ve never held it against any website for dictating how it can be used. There is also gray area here. Every website I’ve ever worked on had to make choices about what it can feasibly support, because business.