With regard to mayday/pan, is there a difference in the extent that external local emergency services are alerted by ATC eg fire service, A&E departments?
In the UK, yes, the category of emergency declared by the controller will affect the response outside the airport. But it varies between different airports depending on the type of operations that go on. For an airport with commercial operations the most significant difference is likely to be that if a full emergency is declared a significant number of ambulances wioll be dispatched to the airport and A&E departments may stop accepting patients and wards may be cleared. Unfortunately the scale of response is nat always scaled to the size of the aircraft so a BN3 may get the same response as a B767.
This is the downside of going for a mayday because it can always be downgraded. And there is at least one instance where a fire vehicle killed a pedestrian (or someone waiting at a bus stop, I think) whilst on its way to the airport for a minor event.