If you write a pile of AJAX and server code which fills our browsers with something that looks vaguely like a windowed desktop, congratulations on your innovation, and good luck rising to the top of the ever-growing pile of these. If your marketing people tell you to advertise this as a "Web OS" bop them on the head with a wiffle bat and tell them to try again. If you, the developer, are tempted to call it a Web OS, change professions this instant.
A desktop-looking thingie running in a browser is just a GUI app. It's an operating system as much as my first cell phone's a Cray supercompter.