A: These two OSs might appear very similar, but they're not the same. Server Core is Windows Server, installed in a "headless" mode, without the Explorer shell or many other components that aren't needed for key role and feature use. Hyper-V Server is a free offering from Microsoft. Hyper-V Server is a locked down version of Windows Server 2008 R2 Enterprise Server Core, with only the Hyper-V role and some additional components and menus.
The free Hyper-V server has no server licensing rights, whereas a Windows Server 2008 R2 installation in core mode still has the same server guest rights as a full installation (four with Enterprise and unlimited with Datacenter). If you intend to run Windows Server OSs, using a Windows Server 2008 R2 Server Core installation makes sense, because you get server guest rights. If you intend to use your hypervisor for non-Windows OSs or client OSs (e.g., your server's a VDI host), using the free Hyper-V Server is probably the most logical.
If you're using Windows client OSs and want to take advantage of RemoteFX, you need to use Hyper-V Server, because server core installs of Windows Server 2008 R2 don't include RemoteFX.
Remember that with Hyper-V Server Windows Server 2008 R2 Server Core, you don't have a local Explorer shell or other management components (although you can remotely run Server Manager). This makes troubleshooting different than for a normal, full server installations, so ensure you're comfortable managing core installations.