It is fundamental to design any interaction. However, since the word 'design' nowadays is applied to everything that exists on earth, it is crucial to highlight that I am addressing the design that follows design processes: Sketch, Wireframe, Mockup, and Prototype
There are unique skills needed in any area of design…but to me…if I design an interactive experience I (also) use media in much the same way I think of it in graphic design, that is, as a way to communicate with someone else.
I suggest asking, what are the design sensibilities both have ?
As a designer, Graphic Design is about visual productions (print or digital) and not User Interfaces (UI) interactions like in web and mobile Applications.
So, we could say that:
Graphic Design is about what we see,
User Interface design (UI) is about the Interfaces that we see (could integrate Graphic Design) and use (digital or physical Interfaces),
Interactive design (IXD) is about the User Interface design and a main focus on what happens between the user (human or not) and the system (tangible or not),
User Experience Design (UXD) is about designing things or processes to alter positivly (or negatively if you have to constrain a problematic behavior) the user experience (and not the experience itself like some people tend to think)