Congratulations on passing your NCLEX-RN!!! Sounds like you will qualify for being a bedside nurse in a NICU. With more experience you might be able to join your hospital's transport team or become a charge nurse (leader of the unit for a shift). A BSN often makes you eligible for entering management positions and is the first step for being able to apply for more schooling to obtain your Masters Degree in Nursing.
These days a person usually needs a MSN (Masters) in order to be a Nurse Practitioner or a Clinical Nurse Specialist. Also it's needed to be a nursing school professor, a researcher, a Case Manager, and other higher level nursing jobs
which are often called "Advanced Practice Nurse" jobs. Many educators and researchers have their doctorate degrees (PhD).
In my experience the Neonatal Nurse Practitioners (NNPs) worked with us in the NICU, performing duties and ordering labs, medicines and treatments under the direction of the Neonatologists. They did lots of more invasive procedures than we staff nurses could do, they would ride with us on the transport team when we expected a super critical patient, and they covered the NICU at nights when the Neonatologists were at home. Our NNPs also helped to staff our hospital's after-care program where our dismissed babies would return for routine check-ups and growth/development checks for the next two years. They were very, very knowledgable about caring for critically ill neonates and most loved to share their knowledge with us too. It seemed like our best NNPs had been staff RNs in a NICU for 5 years or so before going on to NNP school, but that's just my humble opinion... I don't feel any of them were paid well enough for the hours they worked or the stressful work they did. Our Level III NICU had 30 beds and 4 NNPs and 1 CNS.
Our CNS (Clinical Nurse Specialist) was more of a resource person and educator for our unit. She kept up with our skills and educational needs, was responsible for organizing our orientations, kept us knowledgable of new treatments, products, and cutting-edge medical advances in the NICU field. She didn't work a whole lot with us in the unit unless she was showing us how to do things, like changing dressings on percutaneous catheters and things like that. She loved research more than patient contact. Seems like that's the major difference between the two to me.
I'm sure your school's library will have some good references on the different job descriptions. In the final part of your nursing school there will most likely be a course you take which begins to give you more detail about the different nursing jobs available and what is required to enter those positions. Ask your college librarian to help you find some good information. They love to do that kind of stuff for us!
I hope this information has been helpful to you in some way.
By the way, welcome to the USA. We hope you will be happy here and that we can learn as much from you and your experiences as you can from us!