May Day & mayday are two different things, but we talk about both today.
May Day, celebrated on the first of May every year, is a traditional springtime celebration adopted as International Workers’ Day. Traditions vary by country by often involve singing & dancing.
Mayday is “used as a distress call in international radio-telephone communications” (source). The term is most commonly associated with aviation, but is utilized by military & first responders, if necessary.