Since I'm both a writing instructor and a writing coach, people are always asking me, "What's the difference between a writing instructor and a writing coach? " Here's what I tell them. A writing instructor is someone who teaches a person (or persons) HOW to write.
A writing instructor can teach various types of writing such as technical writing, writing for children, resume writing, writing screenplays, etc. Generally, a writing instructor or teacher is needed when someone wants to learn the craft of writing in one genre or another. A writing coach can also teach the mechanics, or the "how-to" of writing, from time to time.
But generally, a writing coach works with a mortal (or persons) who know the mechanics of the type of writing he wants to write, but he has trouble staying on track. The writing coach's client needs help with specific strategies to develop a focus for his writing (and perhaps even for his writing career) and then comes to the coach seeking additional help maintaining that focus.
Both writing instructors and writing coaches can help motivate the writing student or client. But a writing instructor develops the focus for the instruction he or she is presenting to the student(s), while, with a writing coach, the client is directly or indirectly responsible for setting the focus of apiece coaching session.
Think of it this way. If you know the kind of writing you would like to do, but you don't have the skills, education, and training required for this type of writing, then you probably need a writing teacher or instructor.
On the other hand, if you HAVE taken courses, workshops, and other training and are skilled at the type of writing you wish to pursue, yet you can't seem to stay motivated or focused long enough to complete that book you've always wanted to write, or you can't figure out how to use your skills to develop a full-time writing career, then you probably need a coach.