As a current 767 Pilot, and prior C-141/C-17 Pilot in the U.S. Air Force, I can tell you that my airline,which operates worldwide, as well as the USAF, has always taught us that when an emergency situation occurs, the correct verbiage to convey the seriousness of the situation is,
“Call sign, declaring an Emergency”
Flying internationally we were told to say “May day,X 3” or “Pan X3” as the situation warranted. I fly US domestic mostly and in our training we never say “Mayday.” It’s always “ Call sign…Declaring an Emergency”.
This may well be a carryover from the US Military. It’s not a smugness issue or America First sentiment, it’s how we are trained. Good discussion, perhaps this may become an emphasis item and standardization will be established.