Distortion effect pedals push your amp into boosted territory and color your tone, the character of which depends on what pedal you use and what kind of transistor it has.
If a clean boost serves to boost your tone without coloring it and an overdrive takes the boost a step further by simulating your amp’s natural breakup, distortion is the next step beyond that. Distortion effects push your signal into overdriven amp breakup territory, but also modulate and distort your tone as well.
The character of distortion that you get depends on which distortion stompbox you’re plugging into. Most use diodes and transistors to push your signal into clipping territory, and the kind of transistor used—silicon, FET, germanium—has a substantial effect on how the distortion you’re using is going to sound.
What generally separates distortion from its further exaggerated brethren—fuzz—are dynamics and clarity. Fuzz effects push your signal well past the clipping point into territory that makes it harder to hear separated notes. But as with all effects, it mostly comes down to which specific stompbox you’re using.