LOA says that if you're anxious about something happening, you're making it more likely to happen by worrying about it. If you entertain the possibility that you might not get what you want, well, it's your fault if you end up not getting it, because you doubted it. If you have something bad happen to you completely unexpectedly, it's also your fault because you weren't thinking about opposing good things enough. Did you end up in the hospital? Well you should've been thinking more thoughts about how you're perfectly healthy and you never get injured. Intentionally taking precautionary measures against bad things happening to you (or to mitigate the harm if they do happen) counts as thinking about them, by the way! It's completely unscientific and incredibly dangerous. It encourages irresponsible behavior and "positive" delusional thinking, and builds into itself a cult-mentality failsafe that says "if you aren't thinking exactly right 100% of the time, and this doesn't work to get you what you want/prevent bad things happening to you, it's your fault" -- and no one is ever completely free of complicated feelings, anxiety and worries, intrusive thoughts about stuff they don't want. It's not possible to achieve.
Chaos magic says that magic works because you believe in it, that any magical paradigm or form of spell construction you choose to adopt will work for you if you believe in it, and won't work for you if you don't believe in it -- but your belief doesn't need to be permanent, it only needs to be strong while you're working with that particular form of magic. Chaos magic doesn't say your random intrusive thoughts affect reality outside of spellcasting, and acknowledges that training your focus for spellcasting via focused belief is challenging, that it can't be maintained all the time -- but you don't need to maintain it all the time. You maintain it for the duration of your active spellcasting, and then you forget about it. Literally, putting it out of your mind and not obsessively thinking about it while you carry on living your life, once the active spellcasting is done, is a key feature of at least some forms of chaos magic. If something bad unexpectedly happens to you under chaos magic paradigm, it's either just a bit of random chance or a bit of malice from someone else (or possibly a spell misfire or backfire, if you can trace it clearly to a place you failed to close up your loopholes or punched above your weight). Sure, you could've influenced it with spellwork, probably, but you didn't so now it is what it is. Magic is an odds game and you're not the only player on the field (and not all the players are acting deliberately or even sentient, you've got to deal with pesky little things like the laws of physics and the fact that your coworker Jason is an incompetent moron), sometimes stuff happens that's not in your control. If you focused your belief properly casting your spell, and didn't go around specifically doubting the spell itself afterward, and it doesn't work? Lots of possible reasons. Could be that the odds were just stacked too heavily against you by sheer random chance. Could be that someone else was working magic contrary to your goals, and they were stronger/more focused/luckier than you. Or there were more of them.
So, under LOA: if you don't want to be injured in a car wreck, you have to never think about car wrecks. You have to think instead about getting to your destination safely without letting any consideration of an alternative cross your mind, and if you get in a car wreck anyway it must be because you slipped up and thought about it. If you consciously took precautions to avoid getting in car wrecks (such as avoiding particularly busy roads at peak hours and trying not to drive in hazardous weather conditions) or to mitigate harm should you happen to be involved in a wreck (like making sure your seatbelt is always fastened securely and adjusted properly), then you thought about it and it's your fault if it happens, you caused it by thinking wrong.
Under chaos magic: if you don't want to be injured in a car wreck, you can work a spell to decrease the odds that it will happen to you. You need to focus your belief both on the magical structure you choose to use, and on the desired outcome of the spell manifesting for you. If you cast that spell, you then must not worry about whether or not the spell will work; you must believe that it will be effective, or you'll potentially impair its effectiveness. If you end up getting in a car wreck anyway, you might not have focused your spell well enough, but your spellcasting failure didn't CAUSE the wreck, only failed to prevent it. It's also possible that your spellcasting was excellent, but the odds were too strongly against you (did you run a red light turning left without your blinker, on main street at rush hour doing 50mph on an icy day?) or someone else worked a stronger spell that manifested in creating the wreck you were involved in. If you took mundane precautions like avoiding busy roads and hazardous conditions, driving carefully, and wearing a properly-adjusted seatbelt, then you were simply helping your spell be effective by improving the odds it's up against.
TL:DR
LOA says your thoughts always turn into reality no matter what so if bad things happen to you it's your fault and if good things don't happen to you it's also your fault.
Chaos magic says you can focus your thoughts to affect reality by believing in something really hard in short bursts and then not actively doubting it later, and if you fail to get the outcomes you want you could try refining your techniques but also sometimes shit happens.