I'd class him as deep lying playmaker Cs a defensive mid. Massive massive difference in my book.
De Jong would play like kross. You don't call him a cdm.
Let's start with the obvious and undeniable: it would be a dream beyond all belief if we had both Casemiro and de Jong. They are among best in class in their particular roles as destroyer and deep lying midfielder. We could not only make it work, I'm pretty sure most of us here on the caf could just roll the ball onto the pitch without any instruction whatsoever and watch them dominate the opposition in midfield.
That said, you are right to observe that de Jong is a deep lying midfielder (DLM) and Casemiro a central defensive midfielder (CDM). There are differences between the attributes of the skillsets of a DLM and a CDM but both are expected to be highly proficient ball winners, which de Jong and Casemiro are, and both are expected to distribute the ball brilliantly, which both de Jong and Casemiro unquestionably do..
Is Casemiro more the hard tackler than de Jong? Without question. Is de Jong the more accomplished ball carrier than Casemiro? Without question. Are both Casemiro and de Jong both brilliant at picking out the right pass out of the back to restart the attack? I would say yes. De Jong takes that extra touch or two before releasing the ball, which by virtue of releasing the ball higher up the pitch results in a pass that leads directly to a scoring chance, whereas Casemiro releases the ball instantly, requiring that extra pass or two before resulting in a scoring chance.
There is no categorically superior answer between the two approaches to managing the defensive midfield role -- de Jong is more confident in the dribble after the dispossession whereas Casemiro is more confident in the one touch pass after the dispossession. Adding de Jong to Casemiro is almost unimaginable after all these years of dire midfield play, but the point here is that had Casemiro remained at Real and we had brought in de Jong (it seems impossible now) we would have found our answer at central defensive midfield.