To my opinion, FWM is more general concept, when waves with arbitrary frequencies from different spectral regions interact. Three, two or even one frequency can be introduced into the medium, and all the rest can be generated inside. Values of all four frequencies can lie in completely different spectral regions. MI typicallyt implies that input frequencies are within a single and rather narrow bandwidth, and in the course of MI this bandwidth can be broadened but remains a solitay one, i/e/ no separate spectral regions are generated. 

To my opinion, FWM is more general concept, when waves with arbitrary frequencies from different spectral regions interact. Three, two or even one frequency can be introduced into the medium, and all the rest can be generated inside. Values of all four frequencies can lie in completely different spectral regions. MI typicallyt implies that input frequencies are within a single and rather narrow bandwidth, and in the course of MI this bandwidth can be broadened but remains a solitay one, i/e/ no separate spectral regions are generated. 

In my opinion, the MI is generated by a pulse which propagates with high intensity and the pulse is compressed, which causes the generated FWM.

Four wave mixing is the most fundamental process in nonlinear optics. It arises when the two pump waves having same frequency interact. The nonlinear interaction involves the conversion of the pump into a pair of sidebands that are frequency downshifted and upshifted relative to the pump. In the time domain, this leads to a temporal modulation, called modulation instability.

For a complete text-book explanation of MI and FWM, I'd suggest Nonlinear Fiber Optics by Govind P Agrawal.  MI can be interpreted as a 4-wave mixing process that is phase matched by self phase modulation.  Also, in general, as Aleksandrovsky states all four frequencies can be different.  They only need to satisfy energy conservation and momentum conservation.

Kenneth Schepler's reference to Agrawal's book is worth following.

MI can be explained as a FWM process, but does not require that the input signal is pulsed.  Instability is generally only seen in fibres with anomalous dispersion, where the phase mismatch due to chromatic dispersion is offset by the phase shift induced by self phase modulation (SPM) of the carrier.

Any amplitude modulation of the signal results in phase modulation via SPM.  Simultaneously, fibre dispersion converts the newly-generated phase modulation to amplitude modulation.  For anomalous dispersion, the converted amplitude modulation reinforces the original perturbation.  The amplitude perturbation is amplified, with peak gain at modulation frequencies such that the rate of generation of phase modulation by SPM and the phase rotation by chromatic dispersion are exactly balanced.  This can be described as phase matched four wave mixing in which the unmodulated optical carrier acts as a degenerate pump, and power is transferred to two equally spaced Stokes and anti-Stokes sidebands.

For fibres with normal dispersion (negative ps/nm/km), FWM between modulation sidebands and carrier still occurs, but the transfer of energy between carrier and sidebands oscillates along the fibre, with no exponential growth of amplitude modulation.

In FWM, the wavelength separation between the signal and idler is determined by the pump-wavelength, while in MI the frequency separation is dependent on the pump power.