Is autospectrum the same as power spectrum density?
This may be just a matter of semantics. Indeed it is true that "The Fourier Transform of the auto correlation x[n] is identical to the magnitude squared of the Fourier Transform of x[n]". This is just a mathematical identity. 

You could call that the power spectrum density (PSD) but in most practical applications any actual PSD computation will involve some sort of framing and windowing. The choice of framing and windowing will impact the result (and it's a complicated trade off), so there isn't really one clear and unambiguous definition of PSD. 

You can still use the mathematical identity but it needs to be properly adjust with respect to framing, windowing and circular vs. linear convolution.