It is very hard to associated sine wave amplifier power (bench test signals) power ratings when running them with Audio. Typically the amp can deal with a lower speaker impedance loads when working with audio that would cause it to shutdown with a sinewave signal test.
Let start at the beginning.
The purpose of a Audio Amp is to amplify the incoming signal voltage to a higher value (Voltage Gain) and add the necessary current to support a given ohm load up to a given watt rating that the amplifier it design to provide.
Speakers come in many ohm ratings with 8 Ohms and 4 ohms being the most popular.
Amplifiers power output follows ohm’s law in that the current is proportional to the voltage. V = IR The ratio defined by the load in ohms. As the voltage (volume) goes up, so does the current and visa versa. This become important when talking about volume levels and amplifier power ratings. It also plays directly into the discussion of 4 ohm versus 8 loads and what an amp can drive.
Bench testing an audio amp uses two things:
1) A pure resistive constant ohm loads of 8 or 4 ohms are used to represent the target speaker load the amp is specified to work with. The ohm value is constant over ANY audio test frequency.
2) A signal generator that is used to provide an input signal to input of the amp. The signal generator puts out a constant voltage pure tone sinewave signal at a selected frequency.
On the the bench, the signal generator and resistive load are connected to the amp. The amp is power and the signal level the puts out the maximum power for the given load. This verifies the amp has provided the rated output power with no clipping and distortion. The temperature is monitored at full power. Then the signal then lowered to put out 1/3 the amps power rating, the test is run long enough to verify the temperature rise. Both test are looking for temperatures that exceed the design limit. Why 1/3? This is the signal level where a "linear audio amp" is the least efficient dissipating the most heat. No thermal overload, the amp is good. This is how the watt rating of the amplifier is determined. It is the power rating specified for the Amp in the datasheet or manual. The power rating established by this test has NOTHING to do with what the amplifier can put out when working with a real speaker load.
Why?
Unlike resistive test loads, speakers are NOT constant ohm loads which is why the term impedance is used as opposed to resistance. Yes the term Ohms is used to describe them both, but speaker impedance is a complex impedance that comprises properties of inductance along with resistance together. When dealing with impedances, the actual ohm value can very a lot depending on the frequency of the signal being presented to the speaker to reproduce as acoustic sound. Stated another way, 8 ohms is the ideal or average impedance. But there are places in the audio frequency range where the value can drop to 4 ohms or less or skyrocket up to 40 ohms. The 4 ohm is the challenge. In practice a 8 ohm speaker is actually has an average impedance closer to 6 ohms. My point is the speaker ohm load are NOT CONSTANT in terms of ohms and the actual ohm value seen by the amp is a direct function of the specific frequency being produced by the speaker.
With this in mind, a amplifier designer must design the amp to provide MORE current than what a pure 8 ohm resistive load would ever need. It must handle the current of a 4 ohm resistive load to account for the varying speaker impedance. Failure to do that will result in the amplifier going into current limit causing signal clipping and distortion when connected to a 8 ohm speaker load.
Now that the amplifier must drive a 4 ohm load resulting in more current flow, the amount of heat generated by the amp goes up with it. To prevent the amp from overheating working with a 4 ohm load, there is a thermostat of some form that forces the amp to shutdown -OR- forcibly drop the signal level to keep the temperature under control. How fast the thermal overload trips is a function of the thermal dissipation capability of the amp including its thermal mass. Under sinewave bench testing it will trip fast since this static test creates a lot of continuous heat generation.
To protect the amp from speaker impedances below 4 ohms or short circuit, the amp will include a protective current or power limit circuits so it will not blow up.
So far so good, but now lets talk actual music or sounds.
Music and natural sounds are NOT like a sinewave used to test the amp. With music and natural sounds, the average signal level is very low with high peaks. This ratio is called the "crest factor" with defines the ratio between the peak and the average signal level. Simply put, natural sound and music have a high crest factor.
Looking at this from a ohms law current point of view, the high crest factor means most of the current is very low with brief peaks of high current.
Looking at this high crest factor from a thermal point of view, the amp generates very little heat. The high current peaks are not long enough to generate a lot of heat. The amp does not enter thermal overload.
You can take advantage of this crest factor property when thinking about using a 4 ohm speaker load with any given amp designed to drive 8 ohms. The amp may not be cable of driving the 4 ohm load on the test bench at full power, but if you keep the volume levels under control it can drive the 4 ohms speaker just fine. This hold true for the frequencies where the impedance drops. If the volume is high enough, the peak current under 4 ohm load will put the amp into current limit mode clipping the signal. But it only happens during the high peak sound event. It is very hard if not impossible to hear the distortion on any peaks of such short duration. Only if you turn up the volume to high with a 4 ohm load will the average signal level begin to generate to much heat and force a thermal shutdown. You will be able to feel this heat.
Guitar amplifiers are NOT normal amplifiers and cannot be compared to general purpose or professional PA, Stereo or AV Amps. Guitar amps are all about intentional distortion to give the guitar amp a specific unique SOUND. Musical instrument amps do not go through any kind of standardized testing. There is no way to quantify the given amps ability to deal with wide variety of speaker loads. Often the amp and speaker are in a single case making the load a well known variable for the amp. In other words the amp can be optimized to drive that specific speaker as opposed to any speaker. My point is you cannot compare.