For practical purposes, Fuzz = Distortion.
The difference is that "distortion" is a broad term that includes a wide range of effects, while "fuzz" specifically means one kind of distortion: heavy clipping and the addition of odd-order harmonics. A good distortion plugin can do fuzz, along with many other types of distortion.
Distortion does not always result in sustain. Sustain is achieved by greatly amplifying the signal and then chopping it off on the peaks. That's "fuzz", also described as "overdrive". Same concept. Other types of distortion may provide little or no added sustain.