A midwife is a nurse. An OB is an actual Doctor.
Most midwives practice under doctors, although some midwives have their own practice.
Midwife are all natural birth
I had a midwife before but she work out of a hospital,, my midwife did epidurals if needed but could not perform csections
Midwives have more school than just a regular registered nurse, but their training is specifically in healthy pregnancies and deliveries. If you have any serious complications, a good midwife will recommend you to an OB instead. Midwives don't only perform natural births. Mine is happy to do either, although she prefers her clients to birth naturally.
OBGYN's have doctorate degrees and are schooled in all areas of women's health, not just pregnancies. Depending on where you live, most midwives are required by law to practice under an OBGYN.
Also, many midwives tend to spend more time with their clients than OBGYN's and are a little more personalized, but that might just be from my personal experience. :)
Most midwives that work in a hospital are CNM (certified nurse midwife) which have a degree in nursing specifically. But there are midwives out there that are not nurses and don't have a degree in nursing and have their own practice. I have a licensed midwife which she specifies in homebirths/birthing centers but mainly homebirth. An OB specifies in surgery not natural births.