Whoosh.... I heard you call my name dear Crazyheart
A Birth Doula could possibly be someone who has zero training in anything however, most nervous mothers are too picky to choose someone with no training. There are a few good long time organizations who take their work seriously and have a good system of courses, con-ed, supervision etc for a certification process. I was certified as a labour doula, a childbirth educator, and trained as a high-risk antenatal doula (before birth), postpartum doula and lactation educator (not Lactation Consultant).
I have no idea about a Death Doula, except what I've read in the paper. My experience 'doula-ing' would suggest that a death doula has experience - has a body of knowledge about death and good resources to consider, has some sense of counselling/informed consent/walking with people, rather than bossing them around and knowing everything. They might know comfort measures - appropriate ways to soothe certain discomforts, but those would not be medical or intrusive in nature. They might understand family/cultural dynamics and medical processes for supporting/encouraging/suggesting healthy discussions etc. They would certainly have to respect and support the caregiver team, recognizing the boundaries and roles and times to step back, and times to offer assistance. My feeling is that such a support person could be a god-send to families. Sometimes they could be just superfluous, but particularly when medical & community care is really well integrated and attentive.
A good birth doula facilitates, smooths, offers info, quietly watches, physically supports and confidently suggests things for an educated, more confident, supported and team-based birth experience. A good doula knows which hat to put on and which ones to take off, and does so appropriately, based on contracts, agreements, and awareness.
Death Doulas are a fascinating concept, and my experience has made me curious and supportive of the idea. That said, I've been lucky enough to not have any reason to consider it more deeply than that.