Introducing Qubes OS

A hypervisor runs multiple Operating Systems, having each one think that it has access to the whole of the hardware.

A microkernel is one way of writing the kernel of the Operating System, so that each part of it is a separate process, routing messages to each other in a safe manner to get things done, rather than doing direct calls to each others code.

With a hypervisor you wouldn't expect each of the OSes to have any communication with each other at all, whereas with a microkernel you'd expect the different processes to talk to each other a lot.

You can, apparently, repurpose a microkernel as a hypervisor, but I don't know anything about that at all. Presumably the infrastructure is quite similar.

http://x86vmm.blogspot.com/2005/11/xen-and-redhat.html

Both present "virtual machines" to client code. For that matter, so does UNIX, although the UNIX virtual machine has some very complex virtual instructions, like fork(2), exec(2), dup(2), etc. You can crudely map most software platforms on a continuum of abstraction, with something like Python's implicit virtual machine (which is dynamically typed and bound late) at one extreme, and a bare-metal VMM whose interface is identical to that of the underlying hardware at the other.

Both paravirtual hypervisors and microkernels extend the underlying hardware, and they do so at a lower level of abstraction than what we call an OS. In practice, the hypervisors extensions feel more like hardware (they might include device models, virtual memory translation, and interrupt models), while the microkernel's would feel more like software (providing RPC mechanisms, security models, abstractions like "thread" and "process", etc.).

Even in practice the line is grey sometimes. L4 used to call itself a microkernel; now it calls itself a hypervisor.