ChromeOS (not "buildable", pre-shipped) I assume, ONLY on Chromebook and official google devices

ChromiumOS, (build or download built) on anything it runs on

You can't build the browser Chrome yourself, because that is Google's trademark. But you can build Chromium.

There is little difference between ChromeOS and ChromiumOS, so it doesn't matter. What's wrong with something built outside google? Chromium will have all the beta features first, so it'll be better.