This article is intended to address not the parameters of compression, but the types of compression that is acquired through different kinds of gain reduction. GR could be divided into five types based on the electronic method used.
GR gain reduction
VLA Variable Limiting Amplifier
VCA Voltage Controlled Amplifier
FET Field Effect Transistor
Variable Limiting (Vari-Gain) Compressors
Variable Gain compressors include all units that incorporate discrete circuitry other than VCAs, FETs or opto-isolators. Mu is a synonymous term for gain in the world of tubes, and it works by re-biasing a vacuum tube to achieve its compression. These units are known to have a softer knee and smoother characteristics. Vari-Gain comps are quite at home on a mix bus, vocals, or bass guitar.
Example: Manley Variable Mu, Fairchild 660 and 670
Voltage Controlled Amplifiers
A Voltage Controlled Amplifier type of compressor is definitely one of the most versatile and likewise is one of the most common. The VCA can rapidly alter its gain level in response to many different detectors looking at the same signal. It is common practice to employ a VCA type of compressor if one is looking for strict control over the level and dynamics of the signal. They can be just as gentle as any other type of compressor. These are well-known to sound great on many different types of sources, from synths to vocals. They are a safe choice for any application which requires the use of compression.
Example: DBX 160, Focsurite Red, SSL G Bus Compressor
Often referred to as opto compressors, these are isolator type of compressors that use a light bulb (or an LED) to create changes in gain as it corresponds to the incoming audio signal. A photocell (or phototransistor) is then incorporated to track the varying brightness of the bulb and change its gain accordingly. This method is thought to induce smoother characteristics and soften the attack and release times. Compressors using this method are used a lot for bass guitar, vocals, program mix and drums. These compressors offer simple, natural sounding control (unless pressed hard). The compression imparted by these units tends to be very musical due to the use of light transduction. Opticals are also known to be slower and smoother, although colored and aggressive when need-be.
Example: Universal Audio LA2A and LA3A, Tube-Tech CL1B, and Avalon
Field Effect Transistor compressors use a special type of transistor to vary gain. FETs emulate vacuum tubes with a transistor circuit. FET compressors are high-impedance units and have a sound all their own. There are not many examples of these types of compressors because of the expense of the extra circuitry that is needed to operate. These compressors are extremely fast, clean and are studio workhorses. FET compressors are known to be fast-attacking compressors, as well as being smoother and having more control. They are also famous for not really coloring the signal, but this can change depending upon which model is being employed.
Example: Universal Audio 1176 and LA Audio Duel II, Purple Audio MC77
Computer-Based/Digital Compressors (Software)
Plugins are digital representations of outboard analog gear, whether in sound and emulation or merely in conception. They offer the ability to process audio in the digital domain under infinitely precise control. One thing to keep in mind with digital comps is that they are an emulation of analog compressors. Meaning, they are not a direct equivalent but an approximation if you will.
Worth mentioning, there are units that include more than one type of circuit design. These often can't be exactly categorized in the above manner.
Example: Empirical Labs Distressor, and certain Neve models
Hopefully this will help shed some light on how compressors work differently from one to the next, and will help you make better mixing decisions.