No they're different. Head down means baby's head is facing the correct way down towards your cervix, the entrance where baby comes out later on your V.
Baby engage means baby's head has settled down low at your pelvis and you'll start to waddle like a penguin. You might feel easier to breathe also and/or can eat a full meal w/o feeling full too quickly. By this time also you may start to feel contractions. Do walk alot. This really helps you to dilate easier later on.
Anonymous