D.Min at Dallas Theological Seminary:
The program concentrates on developing expertise in the biblical rationale, sociological strategy, and practical implementation of ministry.
The Doctor of Ministry degree is the highest professional degree for those engaged in local church and parachurch ministries, world missions, and similar ministries. (The Ph.D. degree, by comparison, purposes primarily to equip students to engage in scholarly research and teaching.)
It is a 27 credit hour course. I don't know if a dissertation is required.
The Th.D. is a theological equivalent of a Ph.D., generally. DTS replaced its Th.D. with a Ph.D. It is an academic degree, wherein the D.Min. is a professional degree (similar to a J.D., which, although a doctorate, is not on par with a Ph.D. in academic circles).
A Doctorate in Divinity is an honorary degree in America, but there are some foreign universities or seminaries that award it as an academic degree. You can find the degree offered online or at off-the-beaten-path schools or institutions of one type or another, but there are no accredited seminaries or universities that I know of that offer it.
(Before anyone poo-poos accreditation as the end-all, be-all of whether a school or degree is a good one, I'm not arguing the point. I'm just reporting the facts as I understand 'em.)