Tough means an object which is strong and enough to withstand adverse conditions or rough handling.
While, Hard means
solid, firm, and rigid or not easily broken.
Hard is a rigid, which we usually use, when we are to describe a material as a rigid body, it is unbreakable.
While tough, id respectable to the time, it is based on its durability. 
It is tough to handle this situation,
says that, this situation is for just a period,  but, it is tough to cope up with it.
Thus, it differs.

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Hope this will help you.