Distortion, Overdrive, Boost & FuzzEffects that distort the input signal in any way belong to the distortion group of effects
Preamps & Booster
Preamps und booster usually do not produce there own distortion, but rather lift or amplify the input signal in order to overdrive the guitar input signal.
Overdrive Pedals simulate the sound of an overdriven Tube amp. The intensity of the distortion can be anywhere between a lightly distorted sound right up to a fat crunch.
Distortion pedals lay a large portion of distortion on top, the sound is more aggressive and severe.
Fuzz is the original form of the distortion pedal, a simple transistor circuit generates different sounds from dirty to soft singing and right up to crumbly sounds.
The Amp in a Box (A.I.A.B.) Pedals have there own special position in this genre. They simulate certain Amplifier types with all there sounds and characters.