With regards to audio-rate modulation: you will definitely get very different results depending on the target. The positions of the other knobs will also significantly affect the sound of the audio-rate modulation - take a look at fig. 18 to see how drastically different audio-rate modulation of AIR looks depending on the positions of BARREL and FORMANT.
When waveforms other than sine waves are used, or the ratio between modulator and carrier are different, the differences between BARREL, FORMANT, and AIR audio-rate modulation will become much more apparent! The arm spectrograms are pretty purely defined tones, but with different settings, much more intense rumbling and growling abounds!
The similarity between the three spectrograms of A.R.M. is mostly a result of the tuning, however you can still see some significant differences!
For instance, compare BARREL to FORMANT (figs. 13 and 15). For both, when the ARM index is turned up, the first subharmonic (octave below the fundamental) enters. When FORMANT is modulated though, there is significantly more energy across all of harmonics of the subharmonic. However with BARREL modulation, the odd harmonics of the subharmonic have much less energy (the light gray lines between the fundamental’s harmonics) compared to FORMANT modulation. You can also see with FORMANT that there are a few significant diagonal lines where energy changes as the modulation amount increases - it can help to look at it with your head further from the screen to see these more gradual effects!
I definitely encourage you to experiment with different waveforms, tunings between modulator/carrier, modulation amounts, and various positions/sweeps of the knobs themselves as audio-rate modulation is occurring!