More technical (but more correct) is the methodology that a synthesizer uses to arrive at its sound. Of course, there are differences between various synthesizers even within techniques... which gives certain synthesizers a different sound over other types of synthesizers. With that in mind, here is the various synthesizer types around...

Subtractive synthesis

One of the most common synthesizer techniques, found in most analogs and some other types of synthesizers (such as modeling synthesizers). This type of synthesis is achieved by taking a tone with lots of harmonics and filtering them to arrive at the desired tone color. Most sample-playback synthesizers are technically subtractive.

Additive synthesis

Exactly the opposite of subtractive synthesis. Basically, putting together a number of different wave components together (partials or harmonics) to arrive at a particular sound. A specific type of synthesis is Fourier synthesis, which involves mixing together a large number of sine wave harmonics to achieve a specific sound.

Wavetable synthesis

A type of synthesis form which produces a sound through short, cycled samples.

The technique varies between various synthesizers. For the Microwave and PPG Wave, multiple short waveforms stored in a table can be sequenced through a single note, producing rich sounds. The synthesizer also provides the ability to interpolate between various waveforms. For synthesizers like the DW-8000 and ESQ-1, "wavetable" refers to the fact that the synthesizer uses single-cycle waveform samples to produce its sound. For synthesizers like the Wavestation, the reference is to small-sample chunks to produce the sound.

Sound card manufacturers often refer to their soundcards that use sample-playback synthesis as "wavetable" (because the samples are stored in a table in RAM.)

Sample playback (PCM synthesis)

Also known by many other names (AI2 synthesis, etc.), the idea behind this type of synthesis is to take a sample of some kind (whether it be of a synthesizer, acoustic instrument, etc.), and play that sample back as the oscillator (instead of an electrically generated wave). This tends to generate very realistic sounds; the problem is, without the ability to create your own samples (ie, all the samples are stored in ROM), the sound generation options can be limited. Usually, this is an extension of subtractive synthesis.

A sampler attempts to solve this problem by allowing you to create your own samples and play them back via various synthesis options. Samplers are technically sample playback synthesizers with RAM instead of ROM inside; but by enabling you to create your own sounds, the samplers open up a world of new possibilities.

The sample playback synthesis era started with the Roland D-series of synthesizers, which used the term "Linear Arithmetic", implying an additive paradigm. The D-series, like most sample-based synthesizers, is more subtractive than additive though.

Physical modeling

A new form of synthesis that has emerged in recent years. Instead of trying to simulate through an abstract method, the synthesis method tries to physically model the instrument itself, thus providing a very accurate instrument. However, it is often the most difficult to program - and consequently, the hardest to provide an effective user interface for. Nevertheless, analog physical modeling synthesizers recently have appeared with the "classic" easy-to-program knobs et al.

FM synthesis

FM (Frequency Modulation) synthesis, widely popularized by the DX7 and other Yamaha instruments, is a unique type of synthesis. The basic concept behind FM synthesis is that you modulate the frequency of an audio oscillator by the frequency of another audio oscillator. By stacking various oscillators on top of each other, you can get a wide variety of sounds. Yamaha also introduced a modified version of FM called RCM (Realtime Convolution and Modulation); they are very similar, though.
NOTE: Technically, Yamaha's FM is not TRUE frequency modulation; they use a phase modulation technique to achieve results similar to but not quite what you'd get with FM. This is off the scope of a beginner's FAQ topic, but just so you know.

Phase Distortion

Phase distortion was a technique introduced by Casio for the CZ series of synthesizers. The basic concept is to morph various waveforms from their original waveform (saw, pulse, etc.) into a sine wave and back.

Waveshaping

Waveshaping is a technique popularized by such synthesizers as the Korg 01/W. Waveshaping allows you to apply a non-linear function on the original signal, thus offering a wide variety of effects.

Vector synthesis

A way that some of the more powerful synthesizers can create nice sounds through a simple concept. Up to a certain amount of oscillators can be mixed together and (often) realtime controlled through a device such as a joystick. It makes for some nice ways of producing expressive sounds.

Wave Sequencing

Wave sequencing is a feature popularized by the Korg Wavestation. It allows you to sequence through programmable patterns of samples - a concept similar to the "loop-the-loop" partials found in the D-50 and the cycling available in the PPG Wave / Microwave, but with a lot more control, with each sample assigned a level and duration.

VAST Synthesis

A type of synthesis unique to Kurzweil K2000, K2VX and K2500 instruments that combines elements of analog synthesis (filters, pulse width modulation, hard sync, distortion, amplitude modulation) with digital shaper and wrap functions. Multiple configurations of signal paths are available, giving connectivity comparable to a modular synthesizer.

Granular Synthesis

At this time a more abstract concept, granular synthesis is similar to wave sequencing except the snipplets are so short that an actual tone is developed, instead of the rhythm that wave sequencing produces.