An Abstract Data Type (ADT) is:
An abstract data type (ADT) supports only the operations which are defined.
Abstract class is one that may not have definitions of all the objects it have. Moreover it can not be instantiated. To instantiate we have to create a subclass then instantiate the class.
Abstract Data Type is like data structure eg. $STACK$ where we have $PUSH()$ $POP()$ operation defined .
Hence, they are not the same thing.
ADT of any data structure is "what operation stacks you can perform on this data structure."
ADT of stack:
ADT of queue: