Prisilla has a reasonable good definition of HPC. I would change only " it has thousands of computer connected over the network." to "it has thousands of computational processors connected over an internal high-speed network" to distinguish HPC from a cluster of workstations.
HPMC normally is an abbreviation for the chemical Hydroxy propyl methyl cellulose. I've not seen its use in the context of computation before.
The HPC and HPMC both similiar terms.
High-Performance Computing most generally refers to the practice of aggregating computing power in a way that delivers much higher performance than one could get out of a typical desktop computer or workstation in order to solve large problems in science, engineering, or business.
The High-Performance Multi Computing is the aggregation of computing power from multiple heterogeneous computing sources.
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