For "fine-tuning", does the "domain adaptation" approach make sense? I understand "domain adaptation" to be a type of "transfer-learning" technique.
Domain Adaptation:
By applying knowledge obtained from a domain with sufficient teacher labels (Source Domain) to a target domain without sufficient information (Target Domain), a discriminator, etc. that works with high accuracy in the target domain is learned.
(Domain is a term that refers to a collection of data.)
Can I use the "domain adaptation" approach for "fine-tuning" in object detection tasks?

Yes. Fine-tuning is basically one very heuristic approach to doing domain adaptation. In particular, it's an (again, very heuristic) way to do supervised domain adaptation, i.e., where you have labeled data from the target domain. (There are also many unsupervised domain adaptation approaches.)
You may find these slides or this introduction to transfer learning and domain adaptation helpful.
