What is the difference between a Cluster and MPP supercomputer architecture?
In a cluster, each machine is largely independent of the others in terms of memory, disk, etc. They are interconnected using some variation on normal networking. The cluster exists mostly in the mind of the programmer and how s/he chooses to distribute the work.
In a Massively Parallel Processor, there really is only one machine with thousands of CPUs tightly interconnected. MPPs have exotic memory architectures to allow extremely high speed exchange of intermediate results with neighboring processors.
The major variants are SIMD (Single Instruction, Multiple Data) and MIMD (Multiple Instruction, Multiple Data). In a SIMD system, every processor is executing the same instruction at the same time, only on different bits of memory. Essentially, there is only one Program Counter. In a MIMD machine, each CPU has it's own PC.
MPPs can be a bitch to program and are of use only on algorithms that are embarrassingly parallel (that's actually what they call it). However, if you have such a problem, then an MPP can be shockingly fast. They are also incredibly expensive.