It looks like Intel first made IPP with the focus of having the best performance (according to wp v2 is from 2002).
I guess they then found out that many users won’t use it rather than FFTW because it isn’t feature complete (nothing that concerns us - JUCE only wraps power-of-2 ffts anyhow), so they released MKL’s FFT at 2003 with the focus of having the same features and API as FFTW, so that FFTW users could use it as a drop-in replacement. But it appears not to be as fast as IPP.
EDIT: Corrected by Mathieu below that MKL and FFTW’s interfaces differ