In the past some manufacturers have used their own (in a few cases swamp gas) criteria for these specifications. However the accepted International Standard is outlined in the AES (Audio Engineering Society) Standard #2-1984. The rated power of the device is the continuous power that the device can withstand for 2 hours without permanent change in acoustical, mechanical, or electrical characteristics greater than 10%.
Basically according to this standard the Program rating is twice that of the Continuous, and the Peak rating is four times that of the Continuous. Now the Caveat of the standard is that the rating is contingent upon having a minimum of 3 dB of amplifier headroom available. This (at least in my mind) is an audio world diccotomy (not unlike Schrodinger's Cat experiment) in that there may be some conflict between what the standard tells us about the behavior of the transducer in a laboratory test and what we may experience to be true in our particular audio application. In other words YMMV.
Let me try to explain in (nearly) semi-technical terms. Let's say that the loudspeaker is rated at 500 Watts Continuous. That would then be 1000 Watts of Program Material, and 2000 Watts of Peak Power handling . . . BUT in order to meet the 3 dB Headroom criteria of the standard, one must use a 4,000 Watt Amplifier and maintain 3 dB of Headroom above the Peaks. Since uncompressed Live Music has a Peak to Average Crest Factor of somewhere between +14 to +20 dB above where the envelope settles down or where the Program Averages, then this is now somewhat of a Leaning Out Of the Window Contest (one in which you can't win for losing). Practically every Weekend Warrior would Blow-UP a 500 Watt Continuously rated speaker if he were to drive it with a 4,000 Watt amplifier. This is why (generally) the average user should probably have an amplifier as least as big as the Continuous rating of the loudspeaker, but probably NOT more than the Program rating.
It may now be as clear to some as a Turkish Coffee (Hint: You don't drink Turkish Coffee, you TAKE it). But then I am sure there are others who get the bigger picture.
marty