PSD vs FFT of voltage magnitude squared and oscilloscopes
Think about what the auto correlation is doing, looks a lot like squaring. (A thing times itself). Is the Fourier(X)^2 the same as Fourier(X^2) I'm not sure, but suspect yes.

Scopes are probably displaying 20*log10(FFT) which is the voltage power across a 1 Ohm resistor, or dBv. dBw (1 Ohm) = 10xlog10(V^2/1) = 20Xlog10(V) = dBv