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 ran on the zSeries processors, and thus pulled the "z/VM" label, just as OS/390 became "z/OS". Many non-IBMers find this terminology silly, but it's the way it is.
The "VM" term is more generic, and often refers to any VM release (see the VM Fucntion Timeline entry for details on VM releases). Most people use the terms interchangably unless there is a need to explicitly distinguish a release, and as older systems are upgraded or shut down, the generic term "VM" is beginning to refer to z/VM.