They are similar, but not necessarily the same.
Both describe researchers who may use similar methods for understanding the motivators that drive the design physical or software products.
Design Researchers will typically work with traditional ID environments. UX researchers typically will focus more on companies that build software products.
Some of their methods are identical but some pieces are more unique if you are working with hardware or software as your primary business. Likewise you will also see Human Factors engineers which may overlap with some design research activities like prototyping and usability evaluations.