I think that's so, but that relationship between theory and application exists for every technical discipline. Computer scientists vs software engineers, for example. The line is usually blurry; I tend to operate closer to the applied side of software, for instance, but I still think about and am informed by the theoretical side, just as theory is shaped by the experimental results of application.

"Mathematics" is an odd case because what people call "pure mathematics" is upstream of even the theoretical side of technical specialties. Like, what a theoretical mathematician might call an applied mathematician, I might call a data scientist, because they're closer to pure theory than I am, but still closer to technical application than the theoretical mathematician. It's a super-theory that underpins other theoretical domains.