How many different types of synthesis are there? How many matter?
In the earliest days of synthesis there was an idea - additive synthesis. It was only an idea because the technology didn't exist that would make it practical. Now, with digital technology, it is a working reality. Additive synthesis makes sounds from sine wave components, mixing them together, all with different envelopes.
Subtractive synthesis came next. It starts with a harmonically complex sound source such as a sawtooth wave. From this complex sound, harmonics are filtered out until you have the sound you want. Two envelope generators, one for the level and the other for the filter cutoff frequency provide an amazing degree of control.
FM synthesis was the first form of synthesis implemented digitally. A sine wave oscillator, called the carrier, provides the output. But the frequency of the carrier is altered by a sine wave modulator. The modulator can itself be modulated. Carriers and modulators are collectively known as operators; several operators can be combined in various ways in the form of an algorithm.
Wavetable synthesis uses a complex and lengthy waveform sample, which is called a wavetable. To modify the sound produced, different parts of the wavetable can be used, or a sound can transition from one part of a wavetable to another, or even to a different wavetable.
Sample+synth uses a sample as the sound source. This is then filtered and envelopes are applied in a manner very similar to subtractive synthesis.
Physical modeling synthesis mathematically imitates the driver, resonator and modifier of a real acoustic instrument. For example in the trumpet these would correspond to the player's lips vibrating in the mouthpiece, the tubular body of the instrument, and the mute the player inserts into the bell, respectively.
These are the 'big six' forms of synthesis, developed during the heyday of the art. Of course, new types of synthesis are being developed all the time. However, many are just minor variations on the six listed above.
If you learn how to manipulate the big six forms of synthesis, to the point when you are a master of their possibilities, then you are indeed a master of synthesis itself.