As the Commandant said "Guns do not go off by accident.".
Both "accidental discharge" and "negligent discharge" are somewhat judgemental terms; while that may be appropriate in some cases, the term "unintended discharge" would seem a good term to encompass both "accidental" and "negligent" discharges.
If proper safety rules are followed, an unintended discharge, even if one occurs, is unlikely to cause anyone any harm. While firearms do not malfunction often, malfunctions can and do sometimes occur. An unintended discharge in such case may not constitute negligence if care was taken beforehand to ensure that the bullet would be fired in a safe direction.