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The hypervisor for the stand-alone version of Hyper-V is still based on the Windows kernel and is essentially a stripped down version of Windows Server 2008 with no GUI and none of the other normal server services. There is of course also a version which is part of a full install of Windows Server 2008. Hyper-V is the same software running on the same kernel either way. (Edit: This isn't precisely accurate; see the following two posts.)

Of course there is also an edition of VMWare (Player) which runs as an app atop Windows or Linux, but it is a bit different than the hypervisor version.