Back when I finished school and started my career, graphic design was primarily intended for the arena of ink on paper. At any time, media constrains the form of expression. In other words, the instrument confines the art. One cannot fully express dance with a potter's wheel. One cannot fully present an opera with a stick of charcoal.
Graphic Design is even more dependent on media than those other art venues in that its unique purpose is to pursue the audience with an external message. And in that pursuit, it must ride the waves of whatever medium is common.
Nevertheless, the times are different than 40 years ago. Today, digital media of all kinds is displacing ink on paper in the interconnected exchange of ideas. Is there still ink on paper? Yes, depending on how one defines both ink and paper.
The printing industry has been reconfigured by technology throughout is production chain. Everything from banners to buses prints with a message. Digital media continues to bifurcate even as it takes more and more of the communications space.
Graphic designers now must integrate as well as create.
I said all that to say this. A good logo represents in every media presented. But that doesn't mean it has to be entirely the same logo design.