Both of these are discussed in the labor section below. A CNM has a professional graduate degree in midwifery, and has gone through more officially recognized medical training. A CNM always works in partnership with your managing practitioner. This means that she might manage your entire pregnancy and refer you to a doctor only if there's a problem. Or, she may work right alongside your doctor and be with you during all your prenatal exams and tests.
Most hospitals have CNMs on staff.
If you're American, you will have a choice of CNMs on your health plan, just like you have for a doctor. This care is covered by your insurance. These midwives are less likely to be covered by American health plans, and would be paid for independently. For a low-risk, routine pregnancy, this midwife is qualified to act as the managing practitioner as well. Hospitals and primary care physicians will have lists of both kinds of midwives.