Dry firing rimfire
As others have touched on, the firing pin of the centerfire lands in the middle of the chamber, which if it's empty, holds just air.
On the other hand, the firing pin of the rimfire lands on the edge of the cartridge, at the rim, which is supported by the cylinder. Dry-firing the rimfire can not only damage the firing pin, but it can damage the cylinder.
When I called up S&W to ask about dry firing my 617 (.22 rimfire revolver) empty - they said not a good idea.
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