All an amplifier does is amplify the input signal by a fixed amount. We call this fixed amount gain, and since sound is logarithmic in nature and so are decibels we tend to measure gain in dB. Different amplifiers have different amounts of gain.
Another related but slightly different factor is input sensitivity. One amp might require 3v to reach full power, while another might need only 1v.
The term "amplifier" by the way, everything about it applies equally to power amps as preamps. A preamp is nothing more than a power amp with an attenuator.
The attenuator is what most people call the volume control. This can be a potentiometer (trim pot) which is nothing more than a variable resistor. Or it can be a stepped attenuator, nothing more than a whole bunch of different resistors. If your volume control clicks it could be a stepped attenuator. Unless it is a trim pot they thought would sell better if it clicked. We got those too. Point is this: all amps are nothing more than fixed linear multipliers of power, including even preamps.
*** What most people call turning the volume up is in reality turning the attenuation down. ***
Then there is the issue of power output itself. This is the maximum power the amp can put out and is the one thing we have rigorously standardized. This standardization however takes the form of measuring sine waves at specified temperature and duration. It has nothing whatsoever to do with how the amp actually sounds.
Okay so now we have all the basic information to understand. The amp has only so much power. The number the attenuator points at is meaningless. One amp does not "work harder" than another simply because you turn the attenuation down less.
Got it?
