Graph Mining is the set of tools and techniques used to (a) analyze the properties of real-world graphs, (b) predict how the structure and properties of a given graph might affect some application, and (c) develop models that can generate realistic graphs that match the patterns found in real-world graphs of interest.
Data Mining tools are software programs that help in framing and executing data mining techniques to create data models and test them as well.
It is usually a framework like R studio or Tableau with a suite of programs to help build and test a data model.