I am particularly talking about the matplotlib's axes.magnitude_spectrum() function that plots the magnitude spectrum. Is this a representation of the discrete Fourier transform?
FFT (fast Fourier transform) is an algorithm that implements the discrete Fourier transform, in a fast manner. Both computes a "full spectrum" from a signal, which is generally complex. The amplitude spectrum is, up to minor corrections (scaling of components), the magnitude of the "full spectrum".