1. In
A x = new A();
x is an instantiation of A and of type A.
whereas in
A x = new B();
x is an instantiation of B and of type A.
2. The important thing to note here is that (in the second case) if you call x.someMethod(), the method of B will be called, not the method of A (this is called dynamic binding, as opposed to static binding). Furthermore, casting changes only the type, so
A x = new B();
((A)x).run_function(); // Need extra parenthesis!
will still call B's method.
As I said above, you need to include those extra parenthesis since
(A)x.run_function();
is equivalent to
(A)(x.run_function());
