Differences between design research and UX research?

Short answer:
They’re the same.

Longer answer:
Titles that describe design professionals’ roles (especially researchers’ roles) can vary from shop to shop. These titles describe very similar roles and activities: performing research in support of new product development.

The examples you linked describe research activities typical to the beginning of a development process that emphasizes designing to meet human needs and behaviors. People who have those titles (UX Researcher, Design Researcher, etc.) likely practice multiple methods of research based on how far along the development process is. Further along the process these same people might be testing prototypes with users to validate that the embodiment of the design vision performs as defined by the underlying needs research.