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Differentiate in the sense?
Kernel is the basic of a computer. The microkernel is the near-minimum amount of software that can provide the mechanisms needed to implement an operating system. you can view the wikipedia entry to know more about it (just for convenient, if you want to know more, you should read the book " Operating Systems: Design and Implementation ")
you should know the Tanenbaum–Torvalds debate.
kernel is the core part of the operating system which drives the electronic devices and controls its usage based on the input we give and also handles the events running inn the background like scheduling process ,threads ,management of virtual memory ,system call ,file system management which need privileged operations. Coming to the micro-kernel ,it is one one the approach to achieve the kernel functionalities in any optimisized way.The other approach are monolithic kernel and hybrid kernel .And an experimental approach is assembly incorporated kernel. For better concepts refer Operating System principles by peter baer Galvin
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shoot.me has it more or less figured out. You don't differentiate them; a microkernel is a particular way of implementing a kernel. Microkernels typically do the absolute bare minimum of hardware interfacing and leave all of the hard work to helper processes that don't run in kernel space. This theoretically makes a microkernel more secure and less susceptible to crashing, since there is a very small amount of code in the kernel itself.
The downside is, switching from kernel to user space is an expensive operation, so microkernels can be slower. I'm not sure what the state-of-the-art is in microkernels at the moment; some of these problems may have been dealt with already.