Every now and then you’ll hear a Microsoft person, usually from Redmond, talking about Windows Core. Are they talking about Server Core? The answer is no.
We’ll keep this one short and simple. Windows Core is Microsoft’s set of people that develop the central components of Windows. This includes the kernel, security, storage, and hyper-v groups. Mark Russinovich happens to work closely with them.
Server Core is the installation option that gives you a stripped down installation of Windows Server 2008 or Windows Server 2008 R2. It is Windows without the windows, giving you a command prompt to manage the server (or manage it using remote GUI tools). The purpose of it is to reduce the footprint and to reduce the attack surface.