yet I know FM is specific to a single frequency
That is incorrect. The frequency of the carrier varies in FM, which stands for FREQUENCY MODULATION. There does not need to be another carrier which the signal shown in B under FM modulates. That signal, labeled FM, is modulated. That's what frequency modulation looks like.
The image B shows correctly how an FM signal works. The frequency of an FM signal varies with the modulating signal. The maximum variation either way is set by regulation if the FM signal is broadcast. When the modulating signal is at zero amplitude, the frequency of the FM signal is at its midpoint or nominal frequency.
In Image A is the spectrum of an AM broadcast. Why are the side bands so large compared to the carrier? Is this somehow to accommodate the audio bandwidth over a frequency range?
The bandwidth of an AM signal is twice the highest frequency of the modulating (usually audio) signal. In the center is the carrier, and above and below that are sidebands.