The short answer is: it is not related, other than being a similar idea
The VM (Virtual Machine) operating system
What relationship does z/VM bear to VMWare on Intel systems?
The creation of the "z/VM" brand is part of the rebranding process IBM introduced when they realigned all their products into the eServer brand name
VM has gone through several forms in it's 30 year history
There is now an IBM mainframe overview and history presentation available from the SNA publications web site. It gives a history of both the S/3xx hardware and S/3xx operating systems for those folks new to this platform
IBM z/VM ("VM") is the most "fun" operating system running on modern mainframes if you are a programmer/expert-user type of computer person
"Mainframe" is an unscientific term that means different things to different people, but generally speaking, a mainframe is a multiuser business or scientific computer the architecture of which is optimized towards I/O (input and output)
This item describes the overall purpose and function of VM and its descendants. How does the system do what it's supposed to do, what services does it offer, and what concepts and components are part of the basic system?
Prior to z/VM 4, TCPIP was a separately priced product. z/VM 4 integrated it into the base system.
FCON(Full Screen Operator CONsole and Graphical Real Time Performance Monitor) is a very powerful z/VM performance monitor and full screen operator console application. It provides the following functions: