Differences between cpsd and xcorr

Hello, i'm having trouble with a basic signal processing problem : Correct me if i'm wrong, but theorically, calculating the inverse Fourrier transformationof a crosspower spectral density should give me teh intercorrelation, right ?

If so, i do not understand why i get diferrents results when i use :

if true

    Sxy=cpsd(sigM(1,:),sigM(2,:),[],[],Nfft,24000);

    A=sigM(1,:);
    B=sigM(2,:);
    [C,~]=xcorr(A,B,'coeff');

    Rxy=real(ifftshift(Sxy));

end

Shouldn't be Rxy and C strictly the same, if i use the same fft length and sample rate ?