Given that this distinction is entirely subjective (no-one will be able agree on what a test that pigeonholes pages as a 'site' or 'app'), how is it a useful distinction?
Thus I am a complex website engineer. It sounds ridiculous. The webapp developer is domain knowledge wise closer to traditional "application development" than to traditional "website development".
In other words as someone else noted, it is a sandboxed application with
sandbox execution environment == browser IO == REST UI = HTML5 DOM manipulation of the same page
A website (or server app) is a series of HTML5 web apps or HTML5 static pages (JS-less web apps) with navigation logic and inter-app state living in a server app.