For a long time the FAA standard was to say “declaring an emergency.” The thought was if you have English speaking pilots talking to English speaking controllers why use a French word to declare an emergency. In the last few years the FAA has gotten on board with saying Mayday but old habits die hard. I’ve been trying to find when the FAA added Mayday to the vocabulary but haven’t been able to find when that officially happened. Even the current guidance posted above starts out with saying “state the nature of the difficulty” before admitting “Distress and urgency communications procedures are prescribed by the International Civil Aviation Organization (ICAO), however, and have decided advantages over the informal procedure described above.”