Domain adaptation (DA) techniques have the potential in machine learning to alleviate distribution differences between training and test sets by leveraging information from source domains. In image classification, most advances in DA have been made using natural images rather than medical data, which are harder to work with. Moreover, even for natural images, the use of mainstream datasets can lead to performance bias. {With the aim of better understanding the benefits of DA for both natural and medical images, this study performs 557 simulation studies using seven widely-used DA techniques for image classification in five natural and eight medical datasets that cover various scenarios, such as out-of-distribution, dynamic data streams, and limited training samples.} Our experiments yield detailed results and insightful observations highlighting the performance and medical applicability of these techniques. Notably, our results have shown the outstanding performance of the Deep Subdomain Adaptation Network (DSAN) algorithm. This algorithm achieved feasible classification accuracy (91.2\%) in the COVID-19 dataset using Resnet50 and showed an important accuracy improvement in the dynamic data stream DA scenario (+6.7\%) compared to the baseline. Our results also demonstrate that DSAN exhibits remarkable level of explainability when evaluated on COVID-19 and skin cancer datasets. These results contribute to the understanding of DA techniques and offer valuable insight into the effective adaptation of models to medical data.