You are Mayday Fuel if you expect to land at the nearest suitable airport with less than the final reserve (30 mn for jet). Example: your fob is 1h and you need 35 mn to fly to the nearest suitable airport.
You are Minimum Fuel if "committed to land at an airport" (alternate, destination or whatever) meaning you go to that airport and you expect to land at that airport with a fuel not less than the Final Reserve BUT you cannot accept any delay otherwise you would land with less than final reserve.