FFT is a much efficient and fast version of Fourier transform whereas DFT is a discrete version of Fourier transform. ... DFT is a mathematical algorithm which transforms time-domain signals to frequency domain components on the other hand FFT algorithm consists of several computation techniques including DFT.

Why FFT is preferred over DFT?

The FFT provides a more efficient result than DFT. The computational time required for a signal in the case of FFT is much lesser than that of DFT. Hence, it is called Fast Fourier Transform which is a collection of various fast DFT computation techniques.

Does the FFT compute the DFT exactly?

Such algorithms do not strictly compute the DFT (which is only defined for equispaced data), but rather some approximation thereof (a non-uniform discrete Fourier transform, or NDFT, which itself is often computed only approximately). More generally there are various other methods of spectral estimation.