Yes- the interaction is on many levels.
I like to have slightly longer lessons with most of my students (and the parents are mostly willing and able to pay for this). This gives a lot of time to develop relationships. I enjoy my teaching on this level. The kids share with me things about school, ask questions about projects, share their successes and diappointments. The adults do similar. I know this isn't directly what is being asked, but I think it is connected.
I find that teaching is about responding to the needs of the whole student at the given moment. Sometimes the moment requires a little more directive teaching, and sometimes exploration and reaction. Each student is different, because of personality, level, mood, learning style, self-motivation and many other reasons. I relate differently to each one as well, as a reults of the student and how my personality gels with them.
I think a certain amount of teaching needs to be explicit - it saves a lot of time rather than leaving everything to discovery and correction. However, discovery learning is often the deepest learning and I think room needs to be given for this. It provides and stimulates creativity and problem solving - which are very useful in music.
In the background, whether on paper or in my head, I do have a list of things the student needs to learn or correct in the short term and eventually. This is the guiding principal behind my lesson structures and directions, in general. But, the moment by moment is situation dependent - I think everyone has basically said the same.