Those Mysterious FFTs

One question I do not know the answer to, is why many Fourier Transforms are being named ‘FFTs’, which I feel should be named ‘DFTs’.

According to what I read, an FFT is supposed to compute a number of coefficients per octave, while a DFT is supposed to compute a number of them per unit frequency. This would improve the computation of FFTs, by folding them and computing fewer, high-frequency coefficients.

I am seeing Transforms named FFTs, that are still computing the full number of coefficients, per unit of frequency.

Dirk