Fourier theorum says that any wave shape can be recreated as a combination of pure frequencues.
With AM radio, you vary the amplitude of a single pure carrier frequency. With Fourier theorum you could also create the same wave shape by mixing several frequencies together.
The fact is, they are equivalent. If you put a spectrum analyser on the signal you would see all those frequencies appear. The range between the min and max frequency is the bandwidth.
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