Both 자녀 and 자식 mean "sons and daughters, children" The usage is different. 자식(子息) is used for the speaker's children (with 나,저,제) e.g. 저는 자식이 2명입니다. 제 자식은 대학생입니다. 자녀(子女) is used for the other's children e.g. 자녀가 몇 명이에요? 그는 자녀가 없어요. 자식 is also used as the antonym of 부모 e.g. 자식은 부모를 닮는다 부모는 자식을 사랑한다

자(子) means "son", and 녀/여(女) means woman while 식(息) means "offspring". And thus, 자녀 could be translated to "son and daughter" = "children" while 자식 to "offspring" Beware though, 자식 can also mean "bastard" in certain combinations and contexts. e.g. 후레자식 = son of a b*tch. Stick to 자녀, to be on the safer side. 자녀 is the formal expression, hence you should use 자녀 if you are talking about others' children while it would sound awkward if you call your own children 자녀, and in case of your own children, call them 자식.