Page "Discrete Fourier transform" Paragraph 4

FFT algorithms are so commonly employed to compute DFTs that the term " FFT " is often used to mean " DFT " in colloquial settings.

Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.

The terminology is further blurred by the ( now rare ) synonym finite Fourier transform for the DFT, which apparently predates the term " fast Fourier transform " ( Cooley et al., 1969 ) but has the same initialism.