I think i know...rounded is clean, sharp edges show it's starting to clip and at full clipping it becomes more or less square. I've observed this so far.
However, when you EQ that kind of signal with a non-linear frequency response you will notice that the effect of the EQ will alter the waveshape quite drastically. Usually anything resembling "squares" will dissappear because the "flat", DC-like, signal components are attenuated and rising edges are either enhanced or slew limited. This usually does quite a bit of mangling and the waveshape usually ends up looking very different from the usual idea of how a clipped signal looks like. e.g. try googling how a clipped waveform looks like after the tone controls and how it responds to changes of tone controls.
Another issue is feedback. In an amp where you have stages enclosed into a global feedback loop the stages within often try to error correct and they do this by distorting their output signals, basically to counteract the distortion in the overall circuit. So, when you run PA to clipping you may examine clipped waveforms in PA output and waveforms in PI output that look like being distorted. They are not always. The PI's just tries to correct the distortion and increases gain to compensate the clipped portions. This may again look like distortion (because people automatically tend to assume the PI should output just a higher magnitude version of what goes in it) but in essence the PI's actually operating normally and doing it's thing with negative feedback.
Scope just allows you to see the waveform. Equally important point is understanding what you see.
Oscillation? That usually looks like very high frequency signal added up to the original signal. It can be continuous or spurious, where you have just little, short spurs of oscillation striking at signal points where amp's operation is unstable (e.g. clipped or crossover regions, edges of the waveform, etc.)
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