Android and Chrome (OS) operating systems are both Linux-based operating systems. However, Android is designed for touch computing on phones & tablets while the Chrome OS is for Netbooks. Both operating systems focus on security and use a common set of methods to make them more secure they call "sand boxing". Here are some ways each are different yet complimentary and will change security, browsing and mobile application development.
The Google Chrome OS is being created for people who spend most of their time on the Web and will be used with keyboards and light computers or PCs. It will be used mostly for cloud services and no applications will be downloaded to use them on the web. The OS is designed to power computers ranging from small netbooks to full-size desktop systems and will likely turn on about 10X faster than your current Microsoft XP or Window 7 operating system and 5X faster than any Mac Book or laptop. The Google Chrome OS looks and operates similar to the Chrome Web browser and it is much faster than Firefox, Safari or Explorer.
The Android operating system is designed mostly for touch computing and will work on screens that range in size for 3 inches to 12 inches and don't have keyboards. The Android marketplace has application written for the operating system in the marketplace for download. How long will the marketplace last as Chrome becomes more popular and the cloud become the computing standard for mobile. I think the days are number for the iPhone App Store and the Android Marketplace as the mobile web becomes a seamless browsing experience.