http://www.coastalsailing.net/Cruising/Seamanship/Radio/RadioBasics.html:
Please also keep in mind that the Mayday call is only for situations in which life or property is in immediate danger. It is not for calling for help if you've run out of fuel, unless you are in imminent danger (eg, in a channel without an anchor and without alternative propulsion about to go up on rocks). When you call mayday, you are setting the search and rescue operations into immediate action. If you run out of fuel, run aground, or have an engine problem that is not an immediate threat, hail your towing service or the local coast guard for referral to the local towing service. (emphasis mine) You may also consider issuing a securite warning to other vessels. If you perceive danger but it's either not identifyable or not imminent, you may issue a pan pan which gets everyone to listen up for further updates. So the sequence of radio distress calls is as follows:
Least threatening: Securite, securite, securite (you are towing someone and have restricted maneuverability and you want all others to avoid you or to let you know if there's a potential issue)
Moderately threatening: Pan pan, pan pan, pan pan (you have grounded and believe you may be taking on water slowly or are a hazard to navigation)
Immediate danger and distress: Mayday, mayday, mayday (your ship is going down, you've lost someone overboard, your vessel is being smashed on rocks, etc)