ATC / Airports don't use PAN PAN / MAYDAY (if they do they're old school and well out of date) - within airports, they use LOCAL STANDBY and FULL EMERGENCY (level 1-3 depending on size of aircraft) which roughly correlate to the two phrases - in addition there is a Search and Rescue (SAR) phase declared usually by Centre / Approach ATC (INCERFA, ALERFA and DETRESFA) and are especially important when the emergency is outside of the terminal area.
It's very common when dealing with GA pilots for ATC to declare an emergency on the pilot's behalf even if they specifically decline it. Eg "ABC do you require emergency services?" - "Negative". ATC would probably still declare a local standby if there was any doubt. GA pilots often think they have to pay for the services, which is not the case.
At the end of the day it's all about communication and the people on the ground who have the full picture will make an appropriate decision - but almost always if a pilot declares a PAN PAN they'll at least get a local standby and if they declare a MAYDAY they'll get a full emergency. It's more that sometimes a PAN PAN will get a full emergency with consideration to the specific situation.
A pilot cancelling the emergency in the air may not and probably won't result in a full stand down of services, especially if they've already rolled out.
