What does the frequency axis of a Power Spectral Density mean?
The fact that the frequency variable of a power spectral density (PSD) equals the one of a Fourier transform of a &quot;normal&quot; time-domain signal can be seen more easily by considering the following definition of the PSD of a wide-sense stationary (WSS) random process $x(t)$:
$$S_x(\omega)=\lim_{T\rightarrow\infty}E\left\{ \frac{1}{T}\left| \int_{-T/2}^{T/2}x(t)e^{-j\omega t}dt \right|^2 \right\}\tag{1}$$
Note that $(1)$ is just the limit of the expectation of the scaled squared magnitude of the Fourier transform of a truncated version of $x(t)$. So the frequency variable $\omega$ is just the frequency variable of the (squared magnitude of the) Fourier transform.
The Wiener-Khinchin theorem says that the autocorrelation function and the PSD of a WSS random process form a Fourier transform pair.
This answer shows that the inverse Fourier transform of $(1)$ indeed equals the autocorrelation function of $x(t)$.