If a fear effect can kill, that's all we need to know. If you died because if scared your soul out of your body, or because it induced such a massive adrenaline surge that your blood pressure spike caused a spontaneous aneurism in the medula oblongata is a level of detail that the HP system does not attempt to capture.
If a cure light wounds spells heals the sub-lethal damage that fear spell caused by calming your fearful spirit and binding it more tightly to your mortal frame, or by reducing your intracranial blood pressure and removing excess epinephrine from your system is also not modeled.
Carry on.