Back during my seafaring days, I was taught that the proper way to announce a dodgy situation was "Pan Pan" and to announce a real hairball emergency was "Mayday". When I learned to careen across the skies back in the 1960s, I was taught the same way: use "Pan Pan" and "Mayday" I don't know about the military, but my experience was in the civilian aviation environment. I never officially flew for the military.
Of course there could be a bit of Francophobism associated with reluctance to utter the phrase "Mayday", which is allegedly a shortened bastardization of the French phrase "M' aidez moi". On the other hand, Francophiles may object to the shortening/bastardization of any French phrase, considering that use of such a term constitutes an attack on all things French; consequently, such folks would be reluctant to participate in any way in the decline of the French Language by uttering the phrase "Mayday".
Je ne
sais pas.
I have always preferred the use of the "Pan and Mayday" codes because they seem to be fairly precise in their meaning, plus they add a bit of "je ne
sais quoi" to the whole aviation/maritime experience.
Cheers,
Grog