These definitions are taken from Dale and Walker's Abstract Data Types (1996):

Structured relationships are implemented using data structures.

ADTs (abstract data types) are classes of objects defined by a set of values and a set of actions.

So, let's look at a simple C++ class.

class Simple {
public:
        void some_simple_action();

private:
        int x, y;
};

Because it is an implementation, Simple must be a data structure, right? What exactly is the abstract data type of this class?

Second, am I accurate in assuming that ADTs are simply conceptual representations of things, such as the concept of something we may call by name? A stack, for example, has a common notion or even a formal/logical concept. If I write a stack in a certain programming language, what I typed is now a data structure (of this abstract data type).

Is this what I'm thinking it is?