* DD (Doctor of Divinity): This is an honorary degree, typically awarded to individuals who have made significant contributions to the religious community, scholarship, or leadership. It's not earned through a formal program of study in the same way a ThD is. Think of it like an honorary doctorate in other fields (e.g., an honorary Doctor of Letters). It recognizes achievement and service rather than completion of original research.
* ThD (Doctor of Theology): This is a research doctorate. It requires extensive coursework, comprehensive exams, and the completion of a significant, original dissertation demonstrating advanced scholarship in a theological field. It's comparable to a PhD in other disciplines. The focus is on rigorous academic research and contribution to theological knowledge.
In short: A DD is an honorary award for accomplishments; a ThD is a earned research degree requiring significant scholarly work.