Your typical amplifier outputs volts.
not quite right. Voltage (more correctly known as EMF, electro motive force) is the force that pushes energy out of the amp, down the cable, and into the speaker. Therefore, saying that an amp "outputs" volts is incorrect. I know it is confusing because you often see the term "output voltage", but that means the EMF measured at the output terminals, not that it is putting out volts.
Most amplifiers today are designed to act as much as possible like perfect voltage sources i.e. no matter how much energy you try to get out of the amp the voltage will remain constant. This is of course impossible, but what the original OP is referring to is how well a particular amp achieves this goal. There are also amplifiers designed to act as much as possible like perfect current sources including some of the offerings by Pass at First Watt
If an amp can maintain its voltage as the impedance drops then it has to deliver more current to do so. The better it is at doing this the "stiffer" it is. Conventional wisdom is that the stiffer an amp, all else being equal, the better it is. Of course, nothing is ever equal so whether or not this correlates to better performance is debatable and very dependent on the load the speaker presents to the amp.
Two power amplifiers that have the same power supply voltage may not have the same output current.
also not quite right. If 2 amps have identical output voltage into the same load they will have identical output current. It should say that 2 amps with the same power supply voltage may not be able to deliver the same amount of current. I know I am being picky but the lack of succinctness is what causes a lot of confusion among those with a limited knowledge of electronics. Amps do not output volts, they output current. Amps do not "have current", they output current.
Massive current gain stages are usually less linear than more modest stages and require more feedback to keep behaved
this is also incorrect. Typically an amp consists of a voltage amplifier or stages of voltage amplification followed by current gain from the final stage. This current stage is usually some variation on an emitter follower which is extremely linear. It is the previous voltage stages which tend to be non-linear where negative feedback is often employed to make them more linear. It is not unusual to have an amp with less unloaded voltage gain that is capable of delivering a lot more current into a low impedance load than one with a much higher unloaded voltage gain.
