Basically, a MAYDAY is an call for immediate assistance. A PAN-PAN is a call to warn people that you've got a problem and that you may need assistance.
If you make a MAYDAY call and the USCG shows up, they'll be somewhat put out if you don't have a boat that is sinking or on fire or a person with a serious medical emergency... You don't make a MAYDAY call if you've run out of fuel, like a boat did last year... or if you're just tired and want to get off, which has also happened.
BTW, if you don't know the difference between Securité, PAN-PAN and MAYDAY you probably should learn.
calls are basically informational in nature. You might use it when you're about to enter a narrow channel and don't have a working engine, that you saw a drifting log or other potentially damaging flotsam/jetsam/debris. It is also used to report weather updates and such. It is the least urgent of the distress calls.
s are a bit more urgent, and generally, as I posted above, indicate that their is no immediate risk of losing the boat or imminent loss of life. This is often used if you go aground in a soft grounding... like on a sand bar, or if you are taking on water, but the pumps are keeping up with it. It basically says to the boats nearby you... keep an ear out, cause I might be calling for help if I can't deal with this myself. They're a bit more serious than Securités, but not as serious as MAYDAYs.
s are the most serious of distress calls. This should generally only be used when there is imminent danger of losing life or the boat, or the boat has already been lost. If you're aground, with storm waves pounding you onto a rock jetty—this is a MAYDAY situation, not a PAN-PAN. If you're on fire and the extinguishers have failed to stop it... this is MAYDAY situation. If someone has been hit by the boom and one pupil is blown... or had a heart attack... it is a MAYDAY situation...
It is not a MAYDAY situation if you are just tired and want to get off the ship. It is not a MAYDAY situation if you're out of fuel and becalmed. And finally, it is not a MAYDAY situation if you run out of cold beer, even if some of you guys think this is equivalent to the world ending.
BTW, if you use any of these fraudulently or without good reason, you can possibly be charged with fines, the costs of any SAR operations and even jail time in extreme cases.