In essence they are the same, UX just insinuates that the outcome of the process will be a digitally mediated experience.
A design researcher often works in a larger context of society and an academic community and is more knowledge-oriented though I am generalizing a bit.
One difference that we also see is because design researchers typically work in a larger context, they can start to work by implementing design solutions a priori in the context before studying that context, establishing a research through design methodology. For example implementing interactive furniture in public spaces to study the effects on social behavior. While in UX typically it is more solution-testing oriented with single-user situations.