That's a noise plot and not really a waveform, it is a value vs frequency graph (or plot). Similar to a Bode plot.
I would only call a transient (time) response a waveform as that shows the actual shape of the wave (or signal) over time.
But enough nit-picking.
You're correct in thinking that the output_noise = gain * input_noise
However, for the noise-over-frequency plot to be flat, some conditions need to be met:
Both these factors influence the output noise.
Indeed v(onoise) shows the RMS noise at the output.
What you have plotted is the spot noise over frequency. For the total noise you will need to integrate the spot noise over a certain bandwidth.
What the simulator does is:
linearize the circuit (same as in an AC simulation).
calculate the noise voltage / current of each component
calculate what the resulting noise of that voltage / current is at the output (or input in case of inoise)
sum-up all those noise contributions (using sum-of-squares as all noises are uncorrelated).
As this method takes into account the frequency behavior of the circuit, the shape of the inoise and onoise plots do not have to be the same.