Tower is a large building which has usually many floors and nowadays elevators. A building is an structure that has usually only several floors or only one (Notice however that a tower is a type of building). A block is a section in a complex/company/factory/university/etc that contains several buildings, structures (i.e. anthenas), open spaces, etc.

There is no substantive difference between the terms. There is also no difference in those terms between American or British English. A large 20-storey building could be called Tower A, Block A or just Building A. Similarly, a relatively small 4-storey building even could be called Tower A, Block A, or Building A. It is purely up to the organisation/individual who owns or manages the buildings to name them either tower, block, or building. At the end of the day, they all simply refer to a specific building in a given area. Happy learning!