ill 和sick 是形容词,不同的是 ill 只能作表语,而sick 既可作表语,又可以作定语
illness 和 sickness 是ill和 sick 的名词形式,一般作主语,宾语等
如：
他昨天没上学,因为他病了
He didn't go to school yesterday because he was ill/ sick (作表语）
=He didn't go to school yesterday because of his illness/ sickness（作短语介词because of 的宾语）