One could write whole essays trying to answer your post so I'll mostly stick to chaos magic because that's what I know best.
In my understanding chaos magic is basically anarchic, unprincipled and moral-free, 'beyond good or evil' because its practitioners don’t think in these categories. They’re pragmatic and irreverent (what has been often called a 'punk/DIY attitude'), whatever works, works, yields mundane results or produces interesting experiences, whether they involve blissful ecstasy or abject horror. Chaos magic largely lacks a transcedental goal like ascension (RHP) or self-deification (LHP), and one of its hallmarks is paradigm-shifting where you believe in God or gods one week, be an atheist the next and a devout Hindu after that, for example, just to broaden your horizon. "Nothing is true, everything is permitted" is often quoted to describe chaos magic, and it's the attitude rather than the methods that defines chaos magic because its practioners feel free to borrow, appropriate and misappropriate other magics and techniques, no matter how un-woke such cultural piracy may seem these days
What I found frustrating over time is that chaos magic doesn't seem have an overarching spiritual purpose and appears to solely focus on low magic, i.e. doing magic for mundane ends, and that's what it means for many practitioners - you have a problem, so you charge a quick sigil, and when you've hopefully achieved a measure of success, and hurray, you can call yourself a chaos magician. I won't belittle that attitude because I used to be of the same mind for a long time but after many years it felt frustrating because of the long gaps between sigil charging where you do nothing but read classic occult books and snigger at their entrenched ideologies and fuddy-duddy white-lighter mentalities. And with ever expanding relativism, postmodern thinking and rampant eclecticism in the occult arena, closed-minded stereotypical gurus who insist that their methods constitute the Only True Way are becoming rapidly extinct (at least in the occult mainstream, fanatical ideologues still thrive in certain niches).
However, in his seminal "Liber Null & Psychonaut" Peter J. Carroll does write about such a spiritual goal:
The transmutation of the mind to magical consciousness has often been called the great work. It has a far-reaching purpose leading eventually to the discovery of the true will. Even a slight ability to change oneself is more valuable than any power over the external universe. Metamorphosis is an exercise in willed restructuring of the mind.
So the influence of Crowley ("true will") and classic RHP thinking can still be felt here in 1987, even in this 'bible of chaos magic', but this noble goal of self-metamorphosis somehow got drowned out in the youthful exuberant iconoclasm his revolutionary book originally engendered; however, how you achieve that metamorphosis is up to you, whether by serving Kali, Cthulhu or Apollo, whether by mortifying your body, dropping acid every weekend or meditating under an icy waterfall.
As for gods… I'm congenitally unable to take them seriously. I may be able to see them as Jungian archetypes or a superior class of spirits but I find the mere thought that any of them (or their self-proclaimed representatives) should have the power to tell me how to run my life revolting, and the same goes for allegedly holy books or any Laws of the Universe I'm supposed to heed. For a chaos magician, religions are interchangeable paradigms or random belief systems; for me, the only criterion for their relative worth is whether they're empowering or limiting. Gods hardly play any role in my thinking and I create my own magic according to my temperament and mentality and not from a list of 'approved occult methods, or to put it simply, I make it up as I go along.
