You're on the right track - subtractive indeed works by starting with "pure" waveforms, which are then shaped by the filters and envelopes by, well, substracting stuff from them. This might be easier to grasp from actual analog synths - they actually put out a continuous waveform (meaning that without the envelopes and filters, you'll get a monotonous constant sound of them
all the time, not just when you hit a keyboard or something), and only the envelopes (triggered by the keyboard or MIDI/CV messages) make them sound like they have a start and end - basically the envelope's shape is subtracted from that continuous wave.
Additive is a lot more complex, but the basic understanding that all sound is a bunch of sine waves at heart goes a long way: additive "simply" works by adding sine waves together. Do an image search for "additive synthesis", because it's much easier to grasp what happens when you add sines than it is to explain it in words. Additive might actually be the most flexible form of synthesis - but really only on a theoretical level, as it's pretty hard to build an interface that makes it easy. There are some
plugin synths that have managed to get it to a rather easily understandable level - although most of these "borrow" features from the subtractive side of things, because "pure" additive is, well, tough.
Frequency Modulation (FM) is
kind of similar to additive in a way, but instead of just summing them together you'll have sine waves (also other waveforms in
modern plugin FM synths)
modulating the frequency of the other waveforms. Again, do an image search on this to get a basic idea of what happens. Since most if not all FM synths allow you to configure different setups of oscillators (or "operators" as they're called in Yamaha's famous DX line of synths) which all affect each other (or not, depending on the op config) in one way or the other, it swiftly gets tricky to anticipate what actually happens when you adjust one of them. Again, modern plugin FM synths borrow stuff like filters from subtractive synthesis, which makes it a lot easier to quickly change the whole tonality of a patch. The "
classic" hardware FM synths like the DX7 didn't have filters at all. It should be noted that FM syntesis is often possible to an extent on subtractive synths as well - after all, you just need to have one oscillator modulating the frequency of another = basic FM.
Granular - yeah, I thought of mentioning it but decided to leave it out as it's a bit of a niche thing and I'm not sure if there's any kind of
standard on the parts of a granular synth. But the basic idea is that you have a sample that is broken down by the synth into very small "grains" - often just a few milliseconds long - which then form a sound when a big bunch of them are played back at the same time. The parameters of a granular synth often relate to this "cloud" of grains rather than the individual grains, allowing you to
control the duration of the grains, their pitch & placement in the stereo field. This one's
really tricky to explain w/o examples, but let's just say it's more on the experimental side of things, not usually well suited for "normal" sounds but great for soundscapes and ambient stuff. There's a great book on this by Curtis Roads called
Microsound.