> turning discrete samples into intensities at frequencies

This description applies equally well to the discrete wavelet, discrete Gabor, and maybe even Hadamard transforms, which are definitely not, as you assert, "95–99% the same in the end" (how would you even measure such similarity?) So it is not something any reasonable person has ever meant by "the Fourier transform" or even "the discrete Fourier transform".

Also, you seem to be confused about what "discrete" means in the context of the Fourier transform. The ear functions in continuous time and does not take discrete samples.