Here's my knowledge:
A neonatal nurse is one who works with neonates (babies from birth to one month, I believe). A nurse who works in the NICU is a neonatal nurse, and so is a nurse who works in the well baby nursery. However, the distinction we make (at my facility, anyway) is that between neonatal nurses and neonatal intensive care nurses. Ultimately, we're all neonatal nurses, but those that work in the NICU are up one tier, so to speak, as far as patient acuity is concerned.
We do not have mother/baby nurses at our facility, but where I used to work they did this. The M/B nurse was called a PostPartum or Perinatal Nurse and the nursery nurse was still called a Neonatal nurse, even though the PP nurse cared for baby while they were in the room with mom.
At most facilities, a nurse may be required to be pulled to various units (sister units) if they are short. At our hospital, it is the entire Maternal/Child Department, and this includes:
High Risk Antepartum
I work Nurseries 2/3, and can potentially be ordered to work in any of these units (and have), so though I am no expert (Lord, keep me away from L&D!!!) I do find that it helps to be really flexible. I love PostPartum, all Peds units, and Nursery 1.
As a new nurse, I was unable to get a job in a Level I nursery (Neonatal jobs are difficult to get sometimes...nurses seem to tend to get them and keep them forever...you either love it or you hate it, and if you love it, you don't want to work anywhere else EVER!) and so ended up in the NICU, which worked out wonderfully because I fell in love with it. I always felt that if I could get the hang of the harder, more intensive babies, then I could always handle the healthier term babies, which has turned out to be true. Of course, the well nursery has different policies, etc., but when it comes to basically taking care of the baby, I know I can do that and so feel comfortable being pulled there. On the other hand, there are a number of nurses in there who refuse to come to our NICU units because they feel uncomfortable, even in Level 2 with the feeder-growers. Just something to think about. ;>) If you're still a student, try looking for either a job or volunteer position in or around the nursery. This might help you get your foot in the door in case you graduate and there are no listings for nursery openings in your area. Good luck!