A doula is emotional and physical labor support. They work with you before and during your birth to prepare you for labor. Many doulas also do childbirth education. There are also postpartum doulas who come to your house to help for a few days after the birth. Doulas are extremely beneficial to laboring moms and they can be priceless advocates. Doulas do not do clinical work, they don't check dilation, take heart tones, or do anything a doctor or midwife would do. At least they don't in my state.
A midwife is a care provider. A midwife provides prenatal care, catches the baby, and provides postnatal and well woman care as well. A midwife is an alternative to an OB/GYN.
Here is a link about doulas:http://www.doula.com/
And here is a link to MANA, the Midwives Alliance of North America. It has some definitions of the different types of midwives and the midwifery model of care.http://www.mana.org/definitions.html
HTH, sorry it isn't more detailed about doulas. Hopefully a doula will come along and go more indepth.