What is the difference Between Minimum fuel and Mayday Fuel?
The term Minimum Fuel should be used when you currently expect to land with more than the minimum fuel reserves (so everything is OK right now), but any further delay would result in being below minimum reserves when landing. This situation is not yet an emergency and ATC does not need to give you any priority, but they know that keeping you in a holding pattern could result in you declaring an emergency.

The term Mayday Fuel should be used when it is clear that you will land with less than the minimum fuel reserves. This constitutes an emergency and requires ATC to act immediately (this could be priority for landing or diverting you to a different airport, if available).

The ICAO defined both terms in Amendment 36 to ICAO Annex 6 Part I:


  4.3.7.2.2 The pilot-in-command shall advise ATC of a minimum fuel state by declaring MINIMUM FUEL when, having
  committed to land at a specific aerodrome, the pilot calculates that any change to the existing clearance to that aerodrome may
  result in landing with less than planned final reserve fuel.
  
  [...]
  
  4.3.7.2.3 The pilot-in-command shall declare a situation of fuel emergency by broadcasting MAYDAY, MAYDAY, MAYDAY,
  FUEL, when the calculated usable fuel predicted to be available upon landing at the nearest aerodrome where a safe landing
  can be made is less than the planned final reserve fuel.