The MS C++ Docs specify that const types are distinct types from their non-const counter parts. i.e. const int is a completely different type from int, with its own set of rules for how an object of that type can be manipulated. This idea is further supported by the ability to cast e.g. const int to int in the same way you can cast char to int.
In that vein, are references (and pointers for that matter) to types themselves distinct types or are they "built upon" their "underlying type", if that is a fair way to say it.