The world 'child' comes from an old Teutonic word, connected with 'womb'. I'm me Mam's little kid, Just out of factory from earning me brass. Since then, kids have colonised children. They connote informality, and reflect a more relaxed and tolerant attitude towards the young than that suggested by the status of child. Kids' is an indulgent term, permissive, playful.
Children retain something of the regimented wraiths of Victorian schoolyards.
Kids have declared war on children. They are rebels against structures of a childhood which they found oppressive and suffocating. Children should be seen and not heard. Children were subordinate, subject to the vagaries of the adult will. Kids are restive and want to know why.