A kernel is a generic term to represent the core or base of an operating system. Since the operating systems mentioned here are very different, so are the kernels. They are written differently with different goals in mind.
Having said that, no matter what kernel or operating system you are talking about a kernel program shares the same goals no matter what the vendor is. A kernel has to be able to handle booting the system, running tasks, managing resources, and other tasks as required by an operating system.
The kernel is also the resident part of the operating system; it never gets swapped out of memory. Since its function is so important it has to be memory resident all the time.
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