A mayday call will get priority assistance over any other emergencies of lower importance in case of multiple emergencies at the same time on the same frequency.
This is a rare event, but incidents can be related to the same cause as in a multiple engine failure ;-)
Most SOP's require you to Mayday when you got an engine failure on take-off.
While that is not the correct phraseology as you are in an emergency and not in a distress, no one cares less at that moment.
A mayday is a distress call, it's kind of:
"I would like you to know that there is no way we get out of this situation in one piece".