It depends on the firearm. The list of exceptions to BOTH "rules"--that firing-pin springs should always be relaxed, or it doesn't matter--are numerous, because of the wide variations between, say, old double shotguns and modern bolt rifles. The effects of dry-firing also vary considerably, depending on whether the gun's rimfire or centerfire, or the specific design of the firing pin.
These days it's relatively easy to research what effects either leaving the springs set or dry-firing might have. If there's any doubt, a number of companies offer "snap-caps" to safely allow dry-firing. But fired cases will also work, with primer left in place.
