What is the different between the site manager and the construction manager and the project manager in terms of duties and responsibilities

This really depends on the project set-up of the organization. All of the there managers have the same function and responsibilities as reagrd to project management and the realization of the quality and business objectives, though the site Manager report to the Construction Manager and the both the Site Manager and the Construction Manager reports to the Project Manager. 

Depends on the scope of project and how they were appointed, unfortunately job descriptions vary from region to region and company to company.

Site manager is usally responsible for a specific build. The construction manager can be responsible for multiple builds and by default multiple site managers. Project managers tend to deal with aspects of the project not site related i.e. clients / architects etc.