typeof is used to get the type based on a class. That means if you use typeof with object, it will gives you error. You must pass class as parameter parameter. Where GetType is used to get the type based on an object (an instance of a class). Means GetType needs parameter of object rather than class name.
Both of them produce the same information. The difference lies that from where the information is got. typeOf is used to get the type based on class. It will give an error if typeOf is used with the object. GetType is used get the type based on object, which states that geType needs parameter of object.