Is the Auditory Spectrogram the same as the Magnitude Spectrogram?
Edit: As Jazzmaniac pointed out, the below answer I've given is incorrect. See Jazzmaniac's comment for explanation!

The first source you provide contains this image as an example output of the function audspecgram():



This very much appears to be a standard spectrogram of an acoustic signal. To describe it as an 'auditory spectrogram' might just hint to that fact—that it's derived from an acoustic signal. In other words: you are right in suspecting that what is described as an 'auditory spectrogram' in your source is just a spectrogram that is a result of exactly the procedure you describe to obtain it.