These aren't two different things, and in fact, they're really two ways of seeing things rather than things, themselves, at all.
In my usage, randomness is, as Lennon put it, "what happens while you're making other plans." Randomness is a complaint that I make when life sidetracks my intentions.
Chaos is wide-open spaciousness, and by its nature doesn't really permit plans (it's inchoate; that's another way to put it), but it permits action. So as long as I'm willing to fit or surrender whatever it is, chaos functions quite nicely.
Here's an example of the dual application:
The kid sometimes sleeps through the night, but unpredictably. We're never sure if it's going to be 10 hours straight or three wakeups or what, or how long they'll go on or how easy or hard they'll be. Last night it was 2:48 wailing, up til about 4, and then 5:11 wailing, quick put down, alarm goes off at 6:20, the whole household slept through it til 7:20, and then J had to be at work at 8.
So my intentions were:
1. Child sleeps through night (that's always my intention)
2. Wake up, prepare household, take child to daycare at 8
3. Dart over to studio for 8:30-10 "open practice" space
4. Have fabulous practice
5. Go to work, finish grading, give test, get kid, go home
6. Proceed with lovely evening of entertainment, book reading, etc.
In the view of "randomness," I was rudely subverted by the universe on all levels. There was not all-night sleep, there was no daycare at 8, there was late practice (although I did go, I got there at 10), I had a sore, heavy 10 sun salutations and a headstand and a shallow lotus and that's all, I got to work and am about to get the list going, and we'll see how the evening goes.
In the view of "randomness," I can easily become upset and chronically irritated at how unpredictably being a parent governs and in many cases prevents "me" from doing "what I want." And this comes with the ego bleed and with pain and with frustration. Very unfriendly.
In the view of "chaos," however, the universe handed me a total reinvention of my usual morning. A late start plus having to single-parent the kid creates a whole new and uncommon scene. The practice has to move or be surrendered or be adapted, work probably has to be delayed or compacted, and preferences have to shift wildly all over the place so that I don't back myself into a frustrating little corner.
In the view of "chaos," the first thing I do (and I knew this even at 4 am) is toss my intentions out the window, and if the universe happens to see them and read them and feels like respecting them, it'll open a door for me. Otherwise, I handled what there was--I handled what was on the plate rather than trying to choose what I want from the menu. I got the kid to eat breakfast (he likes to play "no" because "no" is interactive, and fun, rather like the way that Owl told us about counting-as-a-game recently) and then we read some books and played for a while and left the house at 9 instead of 8 (because that's how reality wanted it) and got to daycare an hour late, and I got to practice an hour late, and from bad sleep and spotty practices recently, had a mediocre practice, so I emphasized bandhas and attention rather than trying to do anything fancy, and then I went to work, an hour late, and I feel as if I have time to type this, so here it is.
No frustration. Sure, I have no lunch and I need to print out my tests and I probably won't get caught up on my grading for the other class, but whatever, that's just more of what's on the plate. Am I overwhelmed? Guess I better do some midnight grading like I did all last week. So be it. Things move; conditions change; one adapts and makes choices and the consequences become the "plate of tomorrow." I keep setting intentions and then throwing them out; it's hilarious.
There is a ludic character to being in the moment, and high stress forces one into the moment (well unless you go sort of catatonic playing video games or something like that). High-stress action is really weirdly ludic, and that shouldn't make any sense, but it does.