As an ex RAN Aircraft Controller the definitions (from memory) are.
Mayday - Emergency. I am in immediate distress or danger, there is imminent danger to life.
i.e. loss of power or control. Passenger in severe medical difficulties. Engine fire, etc
PAN - Urgency. Situation requires urgent action to avoid imminent danger to life.
Smoke in cockpit, losing fuel, low fuel, EMS warning lights, low oil pressure, fuel pressure.
Hope this helps.
p.s. dont ever think about appropriateness, just make the call. Its better to be heard than not heard. I'd rather be around and be criticised, than be dead and be criticised, at least I have right of reply!;)
My only (very recent) mayday call involved a fair amount of swearing!