Comparing ordinates between FourierTransform[] and Fourier[]

I have a test function ff[t_] := Exp[-t^2 - t]. I have calculated the Fourier transform with FourierTransform[]:

f[\[Omega]_] = FourierTransform[Exp[-t^2 - t], t, \[Omega], FourierParameters -> {1, 1}]

hAdjE Comparing ordinates between FourierTransform[] and Fourier[]

Then, I have calculated the Fourier transform with Fourier[]:

time = Range[1, 1000, 0.1];
Fa = Table[ff[time[[i]]], {i, 1, 1000}];
dF = Fourier[Fa, FourierParameters -> {1, 1}];
ListLinePlot[Abs[dF]]

plWhe Comparing ordinates between FourierTransform[] and Fourier[]

I know how to get the DFT with the x-axis represented by the frequency.

(I’d need some examples representing the relationship between FT continues and DFT.) Why do not coincide me the values ​​on the ordinate between Fourier[] and FourierTransform[]? is a problem of the directive FourierParameters?

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