儿童(ér tóng) - children in Mandarin

儿童 (ér tóng) is the institutional word for children: the one on ticket prices, park signs, hospital departments, publishers' catalogues and government policy. It refers to children as a category, roughly from toddler to early teens.

Because it is a category word it takes no possessive. You say 我的孩子 for my children and 他们的孩子 for theirs. 我的儿童 is not merely odd, it sounds like an official counting a caseload.

So the split is simple. Talking about your own family or someone in front of you, use 孩子 (hái zi) or 小孩 (xiǎo hái). Writing a notice, pricing a ticket or naming a department, use 儿童. Learners who pick one and use it everywhere give themselves away instantly.