Partial Birth Abortion was developed in conjunction with a ruling about when a child was born. A child was deemed to be born after its head exited the birth canal. Killing the child before that was abortion, and could be a thereputic event (if the delivery was breach, and the birth canal was too small/head too large, the woman’s life could be saved, with the option to have another child.) Killing the child after that was infanticide, and treated as murder.
I know of the loony linguistics of partial birth. Your point?