辩论 and 争论, what is the difference? I know they both mean to argue / to debate but why are there 2 different words? I want to know which one should be used in a more casual context i.e. "my brother and I argued" and which should be used in a more serious occasion i.e. "the officers had a debate about it". Also is 辩论 or 争论 used at all when talking about arguing, or is there another, better word for it?
辩 in 辩论 (debate) contains the meaning of 'to convince'
争 in 争论 (argue) contains the meaning of 'to fight'
辩论 is a logic-based debate, each side provides its reason and logic to convince the other side to agree
争论 is a more opinionated/ passionate argument. In short, it is a heated debate/ argument
演化论 vs. 创造论 是一场持续百年的 争论 - Evolution vs. Creation is a centuries-old debate (argument/ fight)
开会決定银行加息与否 是一场 辩论 - Meeting to decide whether banks will raise interest rates is a debate (discussion)
争论(argue) is closer to 争吵(quarrel)
辩论(debate) is closer to 討论(discuss)
According to my intuition, 辩论 is often used as a formal debate between at least two teams, and 争论 can be also understood as a kind of "quarrel, verbal argument". Literally, 辩论 gives me a feeling that these parties involved just try to solve an issue or a problem through 辩论,while 争论 sometimes have a connotation of convincing others by negating their opinions. So, when a person says that another person "和/跟他/她争辩“, the listener may feel offensive.
Plus, in the reality, both words may sound hurtful for some sensitive native speakers. They would not admit that they are having 辩论/争论 with others, and they might say, "我们只是在商量事情，没有争论。".
Sorry for my bad English :D, but I think it's mostly comprehensible(?).
辩论 and 争论, what is the difference?
IMO, 辩论 usually refers to debate. Two teams trying to defencing their stands and convince others. I think you can relate the 'debate' here to the debate competition or some academic discussion.
争论 in other way is a more 'argue' thing. The word 争 here can be understood as a fight to get something. (in my opinion, similar to 争夺) Usually, when you see someone using 争论, it's similar to 辩论 but less formal, more intense, and less organized. It's more aggressive(potentially maybe emotional) compare to 辩论.
I can think of an example, imagine 2 professors attended an academic conference, what they debate at the conference is 辩论, because it's a formal event and I assume they prepare a script or some kind of notes to try to convince others. But after the conference, they walk into a bar and start talking about the same topic. The discussion here is more likely to become a 争论 as what they say now might not be so rational, organized, and maybe added some biased personal opinion/things that haven't been fact-checked.
I want to know which one should be used in a more casual context
Neither I think. (😂) I agree with what @sheliacheng said
in the reality, both words may sound hurtful to some sensitive native speakers
It depends on what kind of discussion you are having. If it's purely discussed, you can use 讨论(discuss where everyone contributing some idea)，商量(discuss where both of you want to reach a consensus)，决定(decide)，想(think), etc.
If it's some intense discussion, you might want (争吵)吵。
Also is 辩论 or 争论 used at all when talking about arguing, or is there another, a better word for it?
I think after you watch the other's answer, you know these two words aren't about arguing. I remember back in secondary school(7th grade - before uni), I joined the Chinese debate team and become the captain of the team. What I learn is not how to debate and win the match, but how to 论. The word 论 means you seriously discuss some topics, focus on the topic and keep drilling down the question. Therefore when you see the word 论, most likely it's not about arguing.
fyi if you want to say argue, just say 吵架 or simply 吵. Sometimes simple is beautiful and powerful.
e.g. 我刚刚和他吵架 (I just argued with him)
我俩昨天吵关于选举的事 (We argued about the election yesterday.)