Post-master's programs as previously stated are those that admit students who already have a Master of Science degree in Nursing. These programs award a Post-Master's Certificate in the particular NP track chosen by the student.
Certificate programs hark back to a time when graduate degrees were not awarded in nurse practitioner programs. At that time, nurses with BSN's, and if I'm not mistaken even ADN's, could be admitted to these certificate programs and become a nurse practitioner. None of these programs exist anymore but I imagine there are still NP's who were educated in this manner and are still currently in practice. That's why your state still has that option to pick on an application for NP certification. On a national level, only graduate degree program prepared NP's are eligible for certification by the national boards.
The official NP tracks are available via the Consensus Model and they are:
Family Nurse Practitioner
Adult-Gerontology Primary Care Nurse Practitioner
Adult-Gerontology Acute Care Nurse Practitioner
Primary Care Pediatric Nurse Practitioner
Acute Care Pediatric Nurse Practitioner
Neonatal Nurse Practitioner
Women's Health Nurse Practitioner
Family Psychiatric and Mental Health Nurse Practitioner