Some people think it’s the same thing, but it’s not exactly true
Chromium OS is the open source development version of Google Chrome OS with some unstable features and untested improvements. Also Chrome OS is shipped only with specific hardware from Google partners.
Next important thing is that Google Chrome OS is officially supported system by Google developers, so you will receive bug fixes and updates after release. This means, it could be more stable and tuned. At these things can be comparable with Windows or OSX.
On the other hand Chromium can be expanded by any developer and is still “up to date”. So we can understand it as the Chromium is one big testing project that provides to Google important data about problems, bugs, unstable things or users improvements tips.
Chromium is an “open source”, that mean, it can be customized and allows any user to tailor it to their needs. Next useful thing to know is that Chromium browser doesn’t send your personal data to Google, as Chrome does. It could be for some people the reason to use it.
Google takes no responsibility for the systems based on Chromium OS and does not help you with any problem. No one is better, because it all depends on your preferences.