I see both
순종 defined as
obey, but surely there is a difference. Is the difference in formality; like, it's situational somehow where
순종 is with parents and
복종 is with law?
I think the term 순종 is much more common in Christian theology than in other contexts. (It can be used in other contexts; it's just not very common.) If you search for "순종하는" in Google, all top 10 hits are about Christianity, whether they are talking about obeying the God or parents.
Also, 복종 is a very strong term: it usually means following someone/something as an absolute authority. So you would use it for a slave obeying their master, peasants obeying the lord, or a military officer following the chain of command, but it's kind of "too strong" to use for obeying your parents or the law.
For parents/law/instructions, the most common expression would be like:
부모님 말씀을 잘 들어야 한다.
법을 지키는/따르는 사람
기내에서는 승무원의 지시에 따라 주시기 바랍니다.
복종 服從 means following and obeying someone's order, command and intention. 服 is submissiveness and 從 means closely following something. 복종 is submissiveness in English and has a bit strong meaning.
Ex) 그의 부모는 아들에게 무조건적인 복종을 요구하였다. His parents require unconditional and absolute submissiveness from him.
순종 順從 means 順 is yielding to and 從 is closely following something. 순종 is similar with 복종 with the meaning of following and obeying something but 순종 has some meaning that 'is motivated by heart' or 'voluntarily follow something without resistance from heart'.
So the difference btw 순종 and 복종 is whether the following is voluntary with my own accord or is motivated or forced by others.