First of all "any-object as string" and "any-object.ToString()" are completely different things in terms of their respective context.
string str = any-object as string;
1) This will cast any-object as string type and if any-object is not castable to string then this statement will return null without throwing any exception.
2) This is a compiler-service.
3) This works pretty much well for any other type other than string, ex: you can do it as any-object as Employee, where Employee is a class defined in your library.
string str = any-object.ToString();
1) This will call ToString() of any-object from type-defination. Since System.Object defines ToString() method any class in .Net framework has ToString() method available for over-riding. The programmer will over-ride the ToString() in any-object class or struct defination and will write the code that return suitable string representation of any-object according to responsibility and role played by any-object.
2) Like you can define a class Employee and over-ride ToString() method which may return Employee object's string representation as "FIRSTNAME - LASTNAME, EMP-CDOE" .
Note that the programmer has control over ToString() in this case and it has got nothing to do with casting or type-conversion.