When I was in graduate school, I was teaching and directing as part of my fellowship. In fact, most of the instructors in the department were called upon to direct on one stage or another in addition to their teaching responsibilities.
A group of undergrads, for reasons that I no longer recall, presented a survey to the many director-instructors of our department asking: Which do you prefer: Teaching or directing? Why? Which do you identify as, a teacher or a director? Why?
After some thought, I answered that I feel that a director- a good one- should be a teacher, and that in theater, at least, a teacher - a good one- should be a sort of director.
The word "educate" comes from Latin sources that mean "to bring out, to lead forth". At its best, directing guides the actor in bringing out the actor's own creativity. Good directing leads forth the artistic team of actors, designers and technicians to finding their own unique, organic whole that is realized in the production.
When I am teaching, I am also working to guide the students to their own discoveries. I prepare and present and propose- and the real learning happens as the students make their own connections and draw their own conclusions. When I am successful in leading forth the students into the new ideas and connections, I will bring out the students' interests and innate abilities and engage their intellects.
Whether directing or teaching, I feel that I can only lead and guide. I create an environment where discoveries can be made and shared.
Ultimately I think it is impossible to "do" directing to someone, or to "do" teaching to someone. The director guides the actor and other theater artists; the teacher guides the students. Director or teacher may offer information or insight, may pose questions or suggest possibilities. In either case, the actor or student, must make the connection within themselves to bring the character to life- or make the learning their own.