MayDay and Pan
Both Mayday and Pan call terms come from the French - Mayday deriving from M'Aidez (Help Me) and Pan deriving from Panne (Breakdown or broken).
Both terms have the same meaning under the internation aviation laws as under the International Maritime Organisation (IMO) - that is to say if the situation does not place the craft and its occupants in grave and imminent danger, then you call Pan-Pan.
In my profession, a Pan call would be for example a major steering failure, or propulsion loss in open water, but you place a nasty rocky lee shore nearby to drift onto and obviously it would be a Mayday.
I can see clearly that a Pan call would have little mileage in the air, as you do not want a graduated response in the field services ("He only needs one truck as he said Pan"). If you have a problem which is not something you are trained to cope with and continue normal flight with, then you have a problem, and it should be a Mayday, giving you full support from the ground.
Sods law dictates if it hasn't gone fully wrong yet, it probably will at 200' on the approach to your chosen piste.
As a pilot, I interpret very differently the rules of when to say what that when I am on the bridge of a superyacht, and a Mayday would come markedly sooner on the 'Oh ******'-ometer from the cockpit that the bridge.
Thats my view of things from sea level. I'm reading with interest the views of those under Company SOP's who have to follow procedures whilst contemplating if they themselves are happy with the developing situation as they decide what to use.
Cheers
That's my view