Are there differences between: Representation and Implementation when talking about ADTs ? How is the representation linked to " the Interface "?

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I am struggling with the Abstract Data Type terminology. I know for a fact that an Abstract Data Type is a data type with the following two characteristics:

1) The objects of the domain of the ADT are irrespective of its "representation"

2) The operations of the ADT are irrespective of its "implementation"

Also, I have come to the understanding that, simply put, Interface = all signatures of the existing methods in the ATD, together with the: pre-/post- conditions and I/O parameters.

I am trying to grasp what "representation" would virtually mean. I believe that "implementation" would be the code written in the .cpp file, whereas the "representation" would simply be the signature of the respective function / class that should be found in the .h ( header ) file?

Thank you and I hope this was not just a manner of speech that misled me!

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