Hi Jim,
I think that to some extent the notions of 'coach' and 'teacher' are interchangeable. I'm not sure that they are synonyms in all circumstances, though.
As a science teacher, when I use the word 'coach' to explain my actions, I am tutoring a person to follow a set of operations that achieve a predictable outcome and that outcome is unvarying. For example, I coach someone in how to multiply two-digit numbers or I coach someone in how division of fractions works.
On the other side of that coin, when I teach someone, I see myself as providing that person with a set of principles that are guided by knowledge and then giving them the freedom to use those principles and knowledge in ways that I have probably never thought of.
My way of thinking is that talented teaching involves elements of coaching as well as elements of facilitating learning. The 'talent' aspect for me relates to a skilled ability to make the complex understandable and, as a consequence, to inspire learners to seek knowledge, to develop skills beyond the classroom and to become their own coaches and teachers.
Thank you for such a thought-provoking question!
Regards,
Noel