The systems in the US and Europe treat infanticide and late-term abortion the same. They are quite coherent, but just don't like to spell out the rules. Infanticide by the mother is illegal, just like late-term abortion, but not much more. If the mother expresses grief at the death, people figure that there's no punishment worse than losing a child, and call it an accident. Many countries have laws on the books explicitly making infanticide a lesser crime than homicide, with a shorter jail sentence. Even when there is a conviction, the sentence is usually suspended.