How is z/VM related to VMWare?

The short answer is: it is not related, other than being a similar idea.

VM and z/VM depend on basic hardware support and the design of the 360, 370, 390, and zArchitecture CPUs to make virtualization of the hardware architecture simple and low-overhead. The simulation of devices and processors is done in software and the CP component of the operating system keeps all the records straight. z/VM and VM emulate only mainframe architecture virtual machines. The overhead for the emulation can be as low as 3% or as high as 25% of a CPU.

VMWare is a similar idea, but emulates Intel PC systems as virtual machines. The Intel architecture was not designed to be virtualized, and has several aspects that are very expensive (in terms of CPU cycles) to emulate. Emulation overhead is typically in the 15-18% of a CPU range, with some operating systems driving it even higher (OS/2 and Netware extensively use features of the Intel chips that are difficult to emulate, Linux uses few of these features and is relatively lightweight).

Both are similar in that operating systems running within a virtual machine simulated by VM or VMWare are unaware that the emulation is present and assume they are running on the bare machine. The difference is in the type of virtual machine that is emulated, and the overhead required to do so.