Difference between reference binding and type conversion in cpp

If the reference binding(initialization or pass into as function argument) is implicit type conversion.

if not, why some casting expression(static_cast, const_cast...) support to cast a non-reference entity to reference and I think it's reasonable to put everything unified. And further more, if reference is a part of type?

struct class A {};
int main() {
    int a = 1;
    static_cast<int &>(a);
    static_cast<int &&>(1);
    const_cast<A &&> (A()); // funny , const_cast<int &&> (1); doesn't work
    const_cast<int &>(a);
    const_cast<int && >(a);
    static_cast<int &&>(1);
}