A midwife and doula have very different roles when it comes to birth.
A midwife is the medical professional of the birth team. She is caring for your health and the health of your baby. She will attend your prenatal visits, keep medical records, give medical advice, oversee the birth, asses when a hospital transfer is necessary, and perform postpartum care for mother and baby.
A doula is a trained birth professional that offers physical and emotional support before, during, and after labor. A doula does NOT provide any sort of medical care or medical advice. A doula is NOT trained to deliver babies. A doula may help you understand what to expect during birth, offer measures to increase your comfort during labor, and be the communication line between you and your chosen birth team.