To start of, let's talk about gain pedals. A gain pedal is one that either increases or reduces the signal that is going through it. The five different types of gain pedals are as follows: distortion, overdrive, fuzz, compression and boost. The first three are the main and most known of gain pedals. Boost and compression can also fall under the category of dynamics.
Firstly lets talk about the distortion pedal which itself adds more gain to the signal that is going through the unit. The signal's wave forms are distorted by the clipping that is being applied by the distortion pedal, this then creates overtones. Some examples of well known distortion pedals would be the Boss HM-2, MXR Super Badass and Pro co Rat distortion.
Moving onto overdrive pedals, these clip the tips of the wave forms adding harmonics or inharmionics. By flattening the tips of the wave forms they add more gain to the signal but not too much as its only the tips of the wave forms that are flattened. Some examples of popular overdrive pedals are the Ibanez tubescreamer, Electro Harmonix Soul food and Boss BD-2 Blues Driver.
Now speaking of fuzz pedals these also clip the wave forms but they clip the wave forms so drastically that they nearly change them into squarewaves. This creates a fuzzy, distorted, lo fi sound. Some examples of well known fuzz pedals are as follow: Electro Harmonix Big Muff, Vox Tone Bender and Arbiter Fuzz Face.
Moving onto compression, this effect compresses/shrinks the signal in order to sustain the signal and to make the sound of the signal thicker. Compression also decreases the variation between note changes in the signal in order to make smoother and tighter transitions. Some examples of established compression pedals are: Boss CP-1X, Jim Dunlop MXR Dyna comp and Fender The Bends pedal.
Lastly lets talk about boost pedals which increases the amplitude of the wave form and amplifies the signal by doing that. This therefore boosts the sound which can also add a more aggressive tone depending on what frequencies are bing boosted by the pedal. Boost pedals are often used to make individual instruments stand out, for example during a solo. A few examples of popular boost pedals are: MXR M133, Suhr Koko Boost and the Keeley Katana.