What is difference between Site Management and Construction Management?

That depends on company's organizational structure. In some projects, site and construction Management are the same. In others, Construction Management is related to each discipline "i.e. Electrical Construction Manager, Mechanical Construction Manager..." and site Management is responsible for the whole site including logistics, Materials, safety .....etc.  

I believe the Site Management deals with following the code, as in to make sure everything is safe and following the inspection guidelines. They oversee the operations on a daily basis.The Construction Manager deal with all the scheduling, cost estimating, laws and ethics.