People frequently talk about their hearing aid's "amplification", but it's important to distinguish between the total amount of sound coming out of your hearing aid and how much energy was added to the sound that went into your hearing aid.
Hearing aids don't generate sound, they simply add to the incoming sound that they can "hear" with their microphones, telecoils or Direct Audio Inputs.
The output is the amount of Sound Pressure Level (in dB SPL) produced by a
hearing aid or FM system. It includes the incoming sound plus the gain added by the hearing aid.
The output is measured with either a calibrated 2cc coupler (HIT) or right in the patient's ear canal (REM). The input stimulus can be "sweep" of tones across the frequency range of the equipment, or specialized stimuli like chirps or artificial speech-like stimuli. Hearing aid manufacturers are required to publish the results of these test to audiologists and to provide them as inserts with the packaging.
Gain is the amount that the aid adds ... in other words, it's the difference between the input level and the output (in dB SPL). It is typical for the gain of linear hearing aids to be measured at 60 dB and also at the maximum volume wheel setting (full on gain). For non-linear hearing aids, it is customary to measure gain at low, medium and high input levels.
The gain added by a hearing aid varies a great deal depending on many factors.
Most hearing aids add differing amounts of gain to the incoming sound at different frequencies so that you get additional gain in frequency ranges where you don't hear as well, but the add less gain in frequencies where you hear better.
Most hearing aids have a clipping function that prevents any gain from being added when the incoming sound exceeds a certain level, so you don't get blasted with painful or hearing-damaging sound levels.
Compression is another feature that most hearing aids use to limit the amount of gain based on the volume of the incoming sound, but, unlike clipping, compression effects d gradually reduces the amount of gain as the incoming volume increases.
Thanks to Brad Ingrao for helping with this definition.