biological mother is "친모, 생모, 친어머니, 친엄마" and the appellation is "어머니, 엄마"
stepmother is "계모, 의붓어머니, 새어머니, 새엄마" and the appellation is "어머니, 엄마 or 새어머니, 새엄마" depending on the intimacy.
mother is "어머니, 엄마" and the appellation is "어머니, 엄마"
mother-in-law is "시어머니,장모" and the appellation is "어머님, 장모님"