A nursery nurse cares for babies in the newborn nursery. An L&D nurse cares for women in labor. A post-partum nurse cares for women who are post-partum and their newborns, quite often. Newborns rarely spend an entire shift in the nursery. An antepartum nurse cares for pregnant women who are admitted for various reasons.
On my unit we have a Transition Nurse. She attends the deliveries, and does the initial bath and medications (vitamin K, and erythromycin eye ointment). Then the baby goes with mom over to mother/baby if all is well, or NICU if there's any issues. The mother/baby nurse cares for both mom and baby. We also have a Well Baby Nursery that is separate from the transition nursery. The nurse or assistant in this nursery is not assigned any patients, but just helps the mother/baby nurses out with assessments if they are busy... monitors phototherapy babies (but again not "assigned" as their patient), and helps with circumcisions. Most of the time the babies stay in room with mom.