"illegitimate child" is a common name, not a formal biological term. Its original meaning is "a man who indulges his wife's affair", and it was written as "forgetting eight" at that time. Later, people used "duck" to refer to or compare with "turtle", because the duck head was green in China's past varieties.
Later, it was also called "tortoise". See (Xue Pan in the Red Chamber: Marry a Man as a Turtle and Husband as a Turtle). Now it is basically used as another name for "turtle" all over the country.