In my mind, genre in writing is primarily characterized by the content of a given work. Thus, two works with entirely different frameworks can still fall under the same genre if the subject matter of the two is analogous. For example, a novel and an essay can both be historical fiction given they are each a fictional narrative in a historical setting, even if one is 400 pages divided into 25 chapters while the latter is only a 5-page short story.
Form, on the other hand, is something I view as the medium and/or structure by which ideas are conveyed through writing. Using my prior example, two works of the same genre would not follow the same form if one is a published novel and the other is a short essay. Writings which employ the same form do not necessarily have to be of the same genre. The example used in class of an editorial is certainly demonstrative of this fact. Another which comes to mind is that of screenplays. Screenplays are a distinct form of writing, but films (or cinema or movies or flicks) can take on any number of topics and are divided into countless genres.
Though many genres may seem to be largely delivered in one form more than others, a given form does not necessarily eliminate the possibility of any given genre, and vice versa.