Nowadays, game music is all digitized. For the most part, it sounds identical between different systems- with only small variations, and the speakers are typically the deciding factor when it comes to sound.
But this was not always the case. There was a time when computers were simply not performant enough- and disk space was at too high a premium- to use digital audio tracks directly as game music.
Instead, if games had music, they would typically use sequenced music. Early on, there were a number of standards, but eventually General MIDI was settled on as a standard. The idea was that the software would instruct the hardware what notes to play and how to play them, and the synthesizer would handle the nitty-gritty details of turning that into audio you could hear.
The result of this implementation was that the same music could sound quite different because of the way the MIDI sequence was synthesized.
The lowest end implementation dealt with FM Synthesis. This was typically found in lower-cost sound cards and devices. The instrument sounds were simulated via math functions, and oftentimes the approximation was poor. However, this also contributed a “unique” feel to the music. Nowadays FM Synth has become popular for enthusiasts of old hardware. Products like the Yamaha OPL3 for example are particularly popular as a “good” sound card for DOS. In fact, the OPL3 has something of a cult following, to the point that source ports of some older games which use MIDI music will often incorporate “emulators” that mimic the output of the OPL3. It’s also possible to find “SoundFonts” which work with more recent audio cards that mimic the audio output of an OPL3, too.
Sample-based synth is the most common form of MIDI synthesis. Creative Labs referred to their implementation as “Wavetable synthesis” but that is not an accurate description of what their synthesizer actually does. A sample-based synthesizer has a sampled piece of audio from the instrument and will adjust it’s pitch and other qualities based on playback parameters. So for example it might have a sampled piece of audio from a Tuba and then adjust the pitch as needed to generate other notes. This produces a typically “Better” and more realistic sound than FM Synth.
Wavetable synthesis is a much more involved form of synthesis which is like FM Synth on steroids; where FM Synth tended to use simpler waveforms, Wavetable synth attempts to reproduce the sound of instruments by having the sound of those instruments modelled with a large number of complicated math functions and calculations as well as mixing numerous pieces of synthesized audio together to create a believable instrument sound. I’m not personally aware of any hardware implementations- though not being anything of a music expert I’m sure there are some- but Software implementations tend to be present and plugins or features of most Music Creation Software.
Personally, I’m of the mind that the best Sample-based Synthesis is better than the FM Synth that seems to be held on a pedestal; they were lower-end cards built down to a price which is why they used the much more simplistic FM synthesis approach, after all. It’s unique audio captured a lot of people playing games using that sort of low end audio hardware, so to a lot of people, FM Synth is how games like Doom or Monkey Island are “Supposed” to sound. I think that Sample-based synth is better- but, on the other hand, that is how I first played most of those games, so I’m really just falling into the same trap.