Yes, different - there are other considerations (the loss of a limb is irreparable even with the monetary compensation). But similar insofar as money is a substitute for what was lost (earning potential, value of stamp) and can be used to replace, to some extent was was lost (earnings, new stamp).
I think you could abstract this back another step - what is money? Basically it's a barter system, reduced to an easily transferable exchange medium. The value of the stamp is the same as the value of anything that the owner of the stamp would accept in exchange (another stamp, a car, an all expense paid trip to Monaco) assuming that a willing buyer would give the same. So it's nothing to do with money except in the abstract sense - we have become accustomed to money as the way to "value" our possessions. I believe that the stamp owner, other stamp collectors, stamp appraisers, and (most likely) judges would be willing to accept that the value of the stamp can be put in dollar terms with at least enough accuracy to render a judgment in the, admittedly somewhat peculiar, case of the crazed stamp destroyer.
Interestingly, at certain times in history even money has lost value to the point of becoming worthless (at which times, the stamp might be a much better possession than literally buckets full of money, and "worth" more in the open market for goods). This is why some invest in rocks - they think that when the paper becomes worthless the tangible property of certain metals dug up from underground will be a better thing to own - silver, or gold.