Distortion, Overdrive and Fuzz
Distortion and overdrive effects create warm, gritty and fuzzy sounds by clipping a guitars audio signal, which distorts the shape of its wave form and adds overtones. Distortion effects are sometimes called gain-effects, as distorted guitar sounds were first achieved by increasing the electric power supply to tube amplifiers. This is why it is called overdrive, and is essentially soft clipping.
Overdrive units created with transistors, much like tube amps, produce "clean" sounds at quieter volumes and distorted "warm" sounds at louder volumes, compared to the "harsh" or "gritty" sound of simple transistor distortion. A fuzz pedal or fuzzbox is a type of overdrive pedal that clips a sound-wave until it is nearly a squarewave, resulting in a heavily distorted or "fuzzy" sound.
In tube amplifiers, distortion is created by compressing the instrument's out-going electrical signal in vacuum tubes or "valves". Distortion effects generally mean both soft and hard clipping, and distortion is caused by perfectly flattened peaks due to saturation or cutoff inside a transistor based unit that does not attempt to smooth the clipping of peaks, will be called a distortion pedal, as the transistor responds to changes in voltage quicker than a tube can, while overdrive pedals, usually consisting of transistor based "Overdrive" pedals exist, in which an attempt at emulating "Tube-like Distortion" is made through extensive electronics and IC design, will retain their typical sine wave form, but will be compressed such that there is less difference between the RMS and the peak of a wave.