The Associated Press stylebook recommends not using the term “late-term abortion,” because “the American College of Obstetricians and Gynecologists defines late-term as 41 weeks through 41 weeks and 6 days of gestation, and abortion does not happen in this period.”
Two things are being conflated here: the clinical term “late-term pregnancy,” which refers to the margins the AP outlines and in the context of natural delivery, and late termination of pregnancy (i.e., late-term abortion), which as everyone following the abortion debate knows refers to abortions that happen at a late stage of pregnancy, typically after 24 weeks, when the baby is viable outside the womb.
Late-term abortions involve particularly gruesome procedures that are distinct from early-term abortions. Perhaps the AP would like to get away from that fact by a change of phrase.