Definition of both terms below, copied and paste here.
JD
A Mayday radio call should be reserved for life threatening situations. These may include, but are not limited to:
Loss, or imminent loss of aircraft control for any number of different reasons
aircraft upset by turbulence;
pilot incapacitation;
spatial disorientation;
control surface or structural failure;
engine failure that will lead to a forced landing/ditching/ejection/bailout;
Or, an onboard fire.
Pan-Pan-Pan
A Pan-Pan call should be used for urgent situations that are not immediately life threatening, but require assistance from someone on the ground. These include, but are not limited to:
Becoming lost;
A serious aircraft system failure, that requires an immediate route or altitude change;
Other emergencies that require immediate attention and assistance from the ground.
This is what the Aeronautical Information Manual has to say about using Mayday and Pan-Pan on the radio.
6-3-1
c. The initial communication, and if considered necessary, any subsequent transmissions by an aircraft in distress should begin with the signal MAYDAY, preferably repeated three times. The signal PAN-PAN should be used in the same manner for an urgency condition.
d. Distress communications have absolute priority over all other communications, and the word MAYDAY commands radio silence on the frequency in use. Urgency communications have priority over all other communications except distress, and the word PAN-PAN warns other stations not to interfere with urgency transmissions.