I think people think* of ChatGPT not as the web UI, but as some mysterious, possibly thinking, machine which sits behind the web UI. That is, it is clear that there’s “something” behind the curtain, and there’s some concern maybe that it could get out, but there isn’t really clarity on where the thing stops and the curtain begins, or anything like that. This is more magical, but probably less wrong, than just thinking of it as the prompt UI.

*(which is always a risky way of looking at it, because who the hell am I? Neither somebody in the AI field, nor completely naive toward programming, so I might be in some weird knows-enough-to-be-dangerous-not-enough-to-be-useful valley of misunderstanding. I think this describes a lot of us here, fwiw)