In North America "Medivac" has to be filed in the flight plan. It's use is goverened by the honour system. That is if you as the pilot feel that the medical urgency requires special handling than you declare the flight a "medivac". Many flights with patients on board are not medivac if there is no particular urgency. Unfortunately this is sometimes abused as I know of one case where a pilot described his flight as a medivac because he had a hot date waiting for him
My last flight as a medivac was an organ transfer with an extremely tight time line. I explained the situation to clearance delivery and they coordinated down the line so I got outstanding handling. There ws no way I could have done the flight any faster
If you have a in flight medical issue that requires expidited handling than you use PAN, or MAYDAY. I had this happen once (suspected passenger stroke) and again ATC were fantastic, giving me direct routings, unrestricted descent and coordinating an ambulance to meet the aircraft.