But is that some more ot less hard clipping threshold or is it like having some increased distortion at 40 dB gain, some more (probably audible) at 80 dB gain and a lot of distortion at 100 dB gain? I understand it could be different for different amps but let's narrow amp designs range to typical modern class A/B designs.
(dB here is not gain - it is a level of sound pressure)
An amplifier clips when the power it is delivering requires the peak output voltages to be higher than the power supply rails (see picture below). At this point it can no longer put out enough volts to accurately reproduce the music waveform and distortion results. The level of distortion increases as the required power output increases, and the tops of the waveforms get more and more flattened off. What level of distortion is audible will probably vary from person to person. However, amps power is often rated at a distortion level of 1% (-40dB) which is well into the audibility range.
So yes - it is a hard clipping level. When you are at the rated power for many amps, they will already be clipping and it will be audible.
By way of an example, I listen at SPL levels of around 75 to 85db (85 when I'm alone in the house and can crank it up a little). So lets take that 85dB
My amp is 100W, I'm listening at 2m and my speakers sensitivity is about 85dB - so according to the calculator I used, it can output 103dB at full power. But lets say that is at 1% THD, and to get distortion free listening it can only get to 10dB less (93dB) (Having said that, 1% distortion is probably not objectionable to most people - especially if it is only hitting peaks/crescendos in music)
So at my "crank it up level" I only have 8dB headroom. Not enough for the peaks of most music, and I'm going to get distortion. At my "sociable" listening level of 75dB I already have 18dB headroom, so am probably fine.
If I sit closer to my speakers, say 1m then I get an additional 6dB of SPL. I now have 14dB headroom, which will be enough for much of the music I listen to, but perhaps not some with high dynamic content such as classical.
Now consider that to get an additional 3dB of headroom, you have to double your amplifier power - and you can see why having more power is always suggested to get the headroom you need.