Windows Core OS is literally the next major OS from Windows (though who knows if they'll just silently upgrade Win10 without a name change or what). Its not small. The point is to create a modularized operating system, built on OneCore, where they can add or remove major features depending on the platform it is deployed to (even features as big as Win32 support).

Andromeda is the codename for their revitalized smartphone effort. Polaris is the codename for their "windows minus the legacy" experience on desktop; no Win32, just UWP, capable of running on significantly less powerful hardware.