Well, as I understand the terms:
parallel computing --- one box with mutiple cpu's attacking the same problem simultaneously.
cluster --- a collection of boxes in the same room pretending to be a single box to the outside world.
distributed computing --- a large collection of systems to handle a very large application. These are all administered by the same organization but seldom are all of the computers in the same room. No requirement to pretend to be a single box.
grid computing --- a very large collection of systems used to attack a very large computational problem. Unlimited numbers of systems can added or removed almost instantly. No requirement for central administation of the boxes on the grid. The systems on the grid may not be dedicated to it and may reside on another grid as well. Think of those screen savers that look for ET. That is probably the world's largest grid.
I agree mostly with Perderabo's definitions. I'd just add examples.
Parallel Computing - A vector supercomputer like a Cray. Older Cray's like the Y/MP and so on. I know they are now making more distributed/clustered supercomputers too, but the big single Cray boxes are the example of Parallel supercomputing.
Distributed Computing - A huge set of systems all doing the same thing. You can add, remove, and replace an individual one without affecting the overall service at all. Something like the huge Google linux farms that handle search requests.
Grid Computing - I can't come up with a better example than Perderabo's SETI screensaver grid. A commercial example would be Sun's grid they rent out for $1 per hour per cpu.
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