A.C.
The midwife is actually able to assist with the birth and help deliver the baby, coach a woman through labor, etc. If they are certified, then they can give medical advice, etc.
The doula is a labor support partner. She cannot give medical advice, and often, while having training, do not have the ability to deliver the baby. The doula helps with comfort measures (knowing various techniques & positions to relieve pressure/pain) and with helping give the birthing mom space to make decisions she comfortable with. But they cannot give medical advice.
For a midwife, you can check out CNMs, which have hospital privileges are usually given rights to deliver in hospitals and also are associated with Ob/Gyn practices.
For a doula, go with a DONA certified doula, who has gone through training.