A data structure is an implementation of the ADT. An ADT can be assumed to be an contract which guarantees certain operations in a promised amount of time. Its doesn't state that how it will layout the underalying data in memory.

Now, its up to the programmer to implement the ADT which is known as Data Structure. For example stack is an ADT and it can be implemented by an linear data structure like Array or linked data structure like Linked List.

Regarding your question I am not sure because its said that:

$Programs = Data Structures + Algorithms $ Reference

So, Stack in itself is not an algorithm but evaluating an postfix expression using Stack is an algorithm.

It seems a subjective matter though.

A data structure is an implementation of the ADT. An ADT can be assumed to be a contract which guarantees certain operations in a promised amount of time. It doesn't state how it will layout the underlying data in memory.

Now, it's up to the programmer to implement the ADT which is known as Data Structure. For example, Stack is an ADT and it can be implemented over a linear data structure like Array or over a linked data structure like Linked List.

Regarding your question I am not sure because it's said that:

$Programs = Data Structures + Algorithms $ Reference

So, Stack in itself is not an algorithm, but evaluating a postfix expression using a Stack is an algorithm.

It seems a subjective matter though.