What is the difference between a doula and a midwife?

There are a lot of myths about doulas. Many people who aren't familiar with midwives and doulas mistakenly think they are interchangeable terms. Some think that doulas are just for home births, or even that a doula would not be helpful if you are having a home birth. Other people think that doulas are only for people wanting an un-medicated or natural birth. Let us define these roles and address each myth one by one.