A construction manager is a construction project manager, there is no difference at all in the roles and the responsibilities. This means that a construction manager is a project manager (so there is no difference between the roles) who is focused on the construction industry.
The construction manager's main role is to manage a construction job. His responsibilities include:
- Creating the budget for the construction project
- Scheduling the construction project
- Allocating the resources
- Procuring the material
- Handling safety requirements
You can see from the above that all of the responsibilities are generic to project managers, with the exception of safety requirements, which is specific to construction (project) managers.
Note that some people in the construction industry believe that construction management is different than construction project management, but they are unable to explain in concrete terms the differences between the two...