Your edit above is correct, Server Core is just one of the options for how you can install Longhorn Server. It is an option that can be used when you want to run a minimal AD, DNS, DHCP, or File server box and not have to manage and maintain all the rest
of Windows on those boxes.
You can still install Server, which includes all the roles, the GUI, CLR, etc.
We are investigating what we can do with PowerShell and Server Core in the Longhorn timeframe, as well as how to keep improving it in future releases.
To reply to some of the earlier questions and posts....
True, you can run Server 2003 headless and never use IE and Media Player, however, the binaries are installed and need to be patched when a patch comes out. With Server Core, the binaries don't exist on the box so no need to patch.
As Iain mentioned in an earlier post, we don't have hard numbers yet. There will be more resources available, since less is installed and running on the system. However, the big benefits are the reduced maintenance and management, the ~70% fewer patches.
We are looking into a including a subset of the .Net Framework for many of the reasons suggested in a future release.
We are also investigating including IIS7 for beta 3. Because there is no .Net Framework, it won't support ASP.NET, but it will support html, isapi, native asp, etc.