Once a Mayday is declared it can be downgraded to a Pan.
The level of response by the airport emergency services will remain the same, they all turn out and prepare accordingly regardless of if it's a Pan or Maday.
The level of reponse by external emergency services is often determined by the aircraft size and/or seating capacity.
We have a Pre Determined Attendance (PDA) system which is recognised by all the external emergency services; any aircraft with a seating capacity of less than 52 seats get a level one PDA, anything with 52 or greater gets level two PDA - if there's any doubt or if it's a freighter it gets the full turn out.