[Toaster]

In essence, these are called Beowulf arrays or parallel tasking arrays.
In almost all cases, the software or "task" must be parallel capable.
They can run any task so long as the above condition is met.
SETI@home is another matter. In this system, each system downloads a "work unit" or more like "a piece of the puzzle". Each system that uses the SETI client software does their own work unit the uploads the result(s) to the server to compile the data from other systems doing other work units. This is NOT parallel tasking/computing.
The BeoWulf arrays, like those in the supercomputing links are another matter. Each system is interconnected and runs THE SAME SOFTWARE or task. This works out to several (even thousands) of systems sharing CPU/Memory and other resources to do a common task. Often, one rather "beefy" machine does what I call "pool data" and does the final assembly to arrive at the end result.

The Cray-1 supercomputer of yesteryear was decomissioned some time ago in preference of the Cray-3 and Cray-4.
These supercomputers used "processor affinity" a method where each CPU in the system could be designated to a particular task.
Its a bit more involved then this but thats the basics.