Chrome vs Chromium

What's the difference between Chromium OS and Google Chrome OS?

Google Chrome OS is to Chromium OS what Google Chrome browser is to Chromium.

Chromium OS is the open source project, used primarily by developers, with code that is available for anyone to checkout, modify, and build.
Google Chrome OS is the Google product that OEMs ship on Chromebooks for general consumer use.
Some specific differences:

The two projects fundamentally share the same code base, but Google Chrome OS has some additional firmware features, including verified boot and easy recovery, which require corresponding hardware changes and thus also don't work in Chromium OS builds.
Google Chrome OS runs on specially optimized hardware in order to get enhanced performance and security.
Chromium OS does not auto-update (so that changes you may have made to the code are not blown away), whereas Google Chrome OS seamlessly auto-updates so that users have the latest and greatest features and fixes.
Google Chrome OS is supported by Google and its partners; Chromium OS is supported by the open source community.
Google Chrome OS includes some binary packages which are not allowed to be included in the Chromium OS project. A non-exhaustive list:
Adobe Flash
Widevine CDM plugin (to support HTML5 EME)
3G Cellular support (but work is on going to address this)
DisplayLink Manager for video over USB (some systems)
Some components are available in both, but as closed source binary-only blobs.  A non-exhaustive list:
Graphics Libraries (e.g. OpenGL) on ARM platforms
Google Chrome ships with its own set of API keys while Chromium does not include any
Users are expected to set up their own
Google Chrome OS has a green/yellow/red logo while Chromium OS has a blue/bluer/bluest logo.