What is the difference between 'typedef' and 'using' in C++11?

They are equivalent, from the standard (emphasis mine) (7.1.3.2):

A typedef-name can also be introduced by an alias-declaration. The identifier following the using keyword becomes a typedef-name and the optional attribute-specifier-seq following the identifier appertains to that typedef-name. It has the same semantics as if it were introduced by the typedef specifier. In particular, it does not define a new type and it shall not appear in the type-id.

They are largely the same, except that:

The alias declaration is compatible with templates, whereas the C style typedef is not.

The using syntax has an advantage when used within templates. If you need the type abstraction, but also need to keep template parameter to be possible to be specified in future. You should write something like this.

template <typename T> struct whatever {};

template <typename T> struct rebind
{
  typedef whatever<T> type; // to make it possible to substitue the whatever in future.
};

rebind<int>::type variable;

template <typename U> struct bar { typename rebind<U>::type _var_member; }

But using syntax simplifies this use case.

template <typename T> using my_type = whatever<T>;

my_type<int> variable;
template <typename U> struct baz { my_type<U> _var_member; }