> for an electric guitar, a triangle wave

That is only true when the string is plucked exactly at the middle - not a regular occurrence. Usually it's more of a sawtooth wave, just without the upper harmonics.

My experience with distortion in guitars is that a huge component here is how different it can sound depending on articulation. Some pieces for example require the player to not alternate their picking, but pluck only in one direction, as the difference is audible.

This is not always the case of course as some amplifiers like those made by Mesa Boogie get their signature tone by exploiting the limited gain-bandwidth product(GBP) of amplifiers, creating an even sound that at the high end of the gain setting is largely without dynamics.

In some cases(like the BOSS DS-1) the manufacturer killed the sound by introducing a technically better amplifier chip - the original had somewhat poor GBP and poor settling time, which in combination produced a nice lowpass filter with a resonance peak at the cutoff frequency, which in turn emphasized articulation.

It's all a surprisingly huge topic.

Articulation is everything! Distortion is compression, and simple things like the I-V curves of a clipping diode or slew limiting from a crappier op amp make a huge difference in the "feel" of distortion, especially with guitar. I love how Boss pedals in the 80s started using a fairly simple discrete op amp design to have greater control over this, as well as stacking on more and more active filtering stages for pre and post emphasis on the distortion.

Designing dirt pedals for guitar is a very humbling exercise in that many seemingly innocuous decisions can have large impacts on the end result. Often times you're bucking what would normally be EE best-practices and exploiting the edges of behavior in components to coax out pleasing nonlinearities. Equal parts engineering and what can feel like sorcery (but usually has a reasonable explanation).

I don’t know anything about the technical details but you can also hear the difference when plucking in different locations on the string very clearly on a classical guitar, to the point where it is an integral part of right-hand technique and is marked on music. Plucking closer to the neck has a very round, resonant sound, plucking closer to the bridge has a very sharp sound, and plucking exactly halfway along the string has a particularly round sound.

As Segovia said, the guitar is like a miniature orchestra https://youtu.be/DJrEl4Nsmsg?si=voLmARBDxGe8iDRo

> Some pieces for example require the player to not alternate their picking, but pluck only in one direction, as the difference is audible.

I still remember the moment in my bedroom 30 years ago trying to play Master of Puppets when I accidentally discovered down-picking.

When a string is plucked near the end where it is attached, the standing wave kind of makes jerking motions. It's just like when you jerk one end of a rope that is attached somewhere. You send a pulse up the rope which comes down again. If you look at one point on the rope, it might be making a quick movement one way, with a slower recovery in the other. This is where we get the sawtooth.

For a sawtooth with all the harmonic, we have to use a bow. A bow directly stimulates a strong sawtooth movement simply because the string adheres to it and releases, many times a second. This will tune itself to a resonant frequency, along with the first bunch of its harmonics.

IMO the main difference between downstroke and alternate picking is that at the same tempo downstroke will have 2 times shorter attack, because the player will have to move their hand 2 times faster.