The only difference, as it stands, between Chrome OS & Android OS is that one is a fully supported, widely popular OS deployed on tens of millions of devices while the other has not yet been launched and doesn't provide with a compelling reason to justify its existence.
Chrome OS should be to Android OS what Windows 7 is to Windows Phone 7 but instead, it is turning out to be the equivalent of Windows CE vs Windows Phone 7.
It's been more than one year now since Sergei Brin, Google's co-founder, confirmed that Android and Chrome OS would merge over time which makes Google's decision to go ahead with Chrome OS as a separate platform even more puzzling.
Steven J. Vaughan-Nichols of ZDnet lists three differences between Chrome OS and Android but two are flawed to some extent. Google might say that Android OS is for Phones & tablets while Chrome OS is for netbooks but we already see that Android can be used successfully on devices with keyboards.
Chrome OS will run cloud-based services rather than having to "download" applications and run then as in a traditional fat-client environment. Nothing however prevents Google from "Chromifying" Android OS; indeed, we'd go as far as saying that Chrome OS is merely a cloud version of Android OS with only one application opened, Google Chrome.
Google Chrome OS will NOT be constantly updated; like any piece of software, it will be updated until it is restarted or rebooted just like Google Chrome is right now. As long as you do not restart your device, it will not be updated.
This is not very different from Android OS which has over-the-air firmware update pushed from time to time. On the other hand, web-based services like Google Apps and Gmail are indeed updated constantly because their DNA is on Google's servers not on a local client.