Where the CDMP is focused on data management with data modeling as a possible specialty, the Data Modeling Certification (DMC) is focused completely and only on data modeling. The DMC is designed solely for data modeling practitioners. Having knowledge of the data modeling chapter of DMBOK2 is helpful (and recommended) for the DMC as well, but a strong working knowledge of data modeling is a prerequisite to passing. Eventually the DMC could become a general data modeling certification, with more advanced specialties within data modeling as add-on certifications such as the Data Vault or UML.
It is similar to the relationship between CDMP and IDMA, where although both are focused on data, they have different audiences, and although there is some overlap, someone most likely would choose both (and not one over the other).
For example, DAMA South Africa offers the DMC and they also offer the CDMP, with no competition between the two certifications. They are positioning the DMC as a complement and sequel to the CDMP, with the DMC being more of a specialty.