As opposed to minimally parallel, one must suppose.
No, that would be maximally parallel. Massively parallel, of hardware architectures, means that there are many, many processing elements, rather than just a few. A ConnectionMachine is massively parallel. A dual-processor server isn't.
I suppose it's like the distinction between a WorkStation and a PeeCee, then: A moving target that slides to be just a bit "better" than what is on your desktop right now.
See Also: CheapMassivelyParallelSequentialSearch