What does it mean that an animal is slaughtered with kosher and Halal methods?

The Ruling on Animals Slaughtered by the Christians Which Were Slaughtered With As-Sar' or by Al-Qasf and the Ruling on Pork Fat

The Ruling on Animals Slaughtered by the Christians Which Were Slaughtered With As-Sar' or by Al-Qasf and the Ruling on ...