It can refer to either.

Any concrete data structure that uses indirection — which means pretty much anything more complicated than dense arrays and records — is indeed a form of graph.

But graphs, and more constrained forms like DAGs and trees, can also be abstract data types, implemented by a variety of concrete representations.

One of life’s little ironies is that implementing a general abstract graph using a general concrete graph whose records and pointers correspond (roughly) 1:1 with the nodes and edges in the abstract graph is often a poor choice.

Moreover, it’s not unusual to have an abstract graph implemented using a non-graph data structure (for example, a dense adjacency matrix) or to use a graph-like data structure to implement an abstract data type whose interface doesn’t look particularly graph-like (for example, a piece table).