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I would posit that every accidental or unintended discharge is preventable... but not all are negligent. In the case of the protruding firing pin, it's not normal to check the bolt face on a firearm every time you load it. You expect it to work properly; when it does not, you are surprised. It was an accident, a failure of equipment. If you holster your shirt in the trigger guard of your Glock and crease your buttocks, that's a bit more negligent. You didn't actively -DO- anything to cause the weapon to fire. You did fail to clear your shirt-tail from the holster. I'm still willing to call this an "accident," albeit one with an element of unintended negligence. However, if you point the weapon and pull the trigger without checking the chamber, that is intentional negligence, and any lead leaving the barrel can NOT be called an "accident."
So, way I see it, you have three levels of unintended discharge, instead of two.

AFD - Accidental Failure Discharge
AND - Accidental Negligent Discharge
WND - Willful Negligent Discharge

One can muddy the waters even more by picking and choosing examples, but it mostly falls into those categories for me. I would also bet that the AFD is by far the rarest, and that a lot of ANDs were really WNDs, but played down to alleviate blame.