I believe the two positions are quite similar in a lot of ways. I see the clinical pm as a subset of project managers as a whole. According to progenics pharmaceuticals, these are the primary responsibilities of a CPM:

-Leads planning and communication with cross-functional teams to ensure proper execution and conduct of the trial.
-Serves as primary contact and resource for LCRA, CRO and vendor personnel. Supports selection and provides oversight and management of CROs, consultants and vendors.
-Tracks and reports on the progress of assigned clinical trials including budget and timelines.
Preparation, oversight and review of study related documents.
-Works with Clinical Trial Managers, Data Management, Clinical Trial Assistant and Document Control Specialist to create and manage study related documents.
-Co-monitors with CRO’s Monitors to evaluate and ensure quality of CRO Monitoring Team. Ensures that studies are conducted in accordance with the protocol, GCP / ICH guidelines, FDA regulations and departmental SOPs.
-Organizes (or assists with organizing) and participates in meetings – i.e. Study Team Meetings, Investigator Meetings, Monitors’ workshops, and CRO Training.
-Participate in the preparation, review, updating and training of SOPs.

I believe the main difference that distinguishes CPM’s from other project managers is the amount of regulation that they need to be aware of and close involvement of the FDA.