Just to add some more information, from the Coast Guard's perspective, they use the phrase "Pan Pan" when issuing an Urgent Marine Information Broadcast (UMIB).
Saying "Pan Pan" is kind of like saying "Hey, listen up! This is really important and could mean someone is in trouble!"
As opposed to when the CG uses the phrase "Securite, securite, securite" which indicates that they are going to make a general Safety Marine Information Broadcast (SMIB). That's kind of like saying "Hey, listen up! This is important..."
From the boater's perspective, I don't feel that it's important to use "Pan Pan" on the radio. Either you are going to call Mayday because they are in imminent danger and need help, or you can call out for the Coast Guard directly if you want to pass along some kind of safety information about yourself or someone else.
Example 1:
"Mayday, mayday, mayday. This is the vessel Money Pit, at position xx - xx.xxx / xx - xx.xxx, with four people on board. We are taking on water and are in need of immediate assistance."
Example 2:
"Coast Guard, Coast Guard, Coast Guard. This is the vessel Money Pit. We are at the entrance of XYZ Harbor and request that an ambulance meet us at the pier for a serious laceration." (the idea being that you need help, but don't need the CG to come out and airlift the patient.