While subjectivity is an object of concern, I think that because of how music fundamentally works, and because of certain musical conventions to which most people generally ascribe a sound (harmonic minor being Egyptian, or the descending natural 7th of HM sounding "baroque"), a general template can be created to achieve a basic sound. For instance, a certain word can be connoted differently from person to person, but the word's fundamental meaning is still intact, if that makes any sense. I say "most people" because of how similar feelings are achieved in both Western and Eastern music (e.g. Goldeneye and Castlevania respectively). Some types of sounds just, in my mind, can't be mistaken as another kind, such as someone feeling like a moderate tempo song in a predominantly major key is terrifying.
As for the question though, a harmonic representation of chaos could be done in a lot of ways. It can either be approached intellectually or, I guess you could say, "intuitively." By intellectually, I mean making the song itself chaotic and disharmonious, and by intuitively, I mean using a discernible structure, but consistently redirecting the flow of the song with either abrupt modulation, dissonant melodies/harmonies or both rather than through an actual chaotic structure so that the chaos is more felt than acknowledged.
If I were express something "chaotic" I'd maybe prep the harmony with a consonant melody and progress in diminished, augmented or mmaj7 chords and false cadences into these chords. Like I said though, that would just be a template. I'd by no means use a "word bank" so to speak to make a song, since I think that'd be a disingenuous way to approach music. Briefly, my personal template for composing a "chaotic" song would be alternating time signatures, use of chromatic harmonies and melodies, false cadences, symmetric scales and possible tonal scales to create contrast and emphasize the dissonance of the symmetric scales.
Rhythmically, there're a million ways. Alternating time signatures, syncopating on the off-beats, asymmetric note patterns. Words I keep in mind in addition to "chaotic" would be asymmetry, unpredictability and dissonance.
Though, "chaotic" can mean a lot of different things, so the musical armory for creating a chaotic sound is pretty stacked. Though, that's another good thing to mention, is the decomposition of certain words into more basic, definite ones. To me, the epitome of chaotic is either a frenetic pace with no particular key destination or an ambient soundscape. Tone can be very important as well.
And when you ask if the two differ, what do you mean?
Oh, also, pretty familiar examples of what I feel represent "chaos" in music:
- Curse ZoneIt has a solid melody, but it's mostly chromatic, never resolves and satisfies a lot of what I'd consider "soundscapes," with asymmetric ornaments.
http://www.youtube.com/watch?v=1wRi51ItCag - A Man of Artificiality
A lot of rhythmic ornamentation that gets contrasted by the brief Minor resolution.
Sorry for the huge post, but "chaos" is just such a broad term.
I agree with the pedal tone, especially. The constant alternation of dissonant/consonant really bends your ear.
- Golbez, Clad in the DarkUematsu spells out a diminished arpeggio on the accented notes. Such a cool sound.