One of the ways to distinguish between coaching and mentoring is in what type of learning takes place in each of these strategies.
Coaching is about behavior, so we can call the type of learning that takes place in coaching "transitional." It's about doing things differently. This can mean removing existing behaviors that are not working and replacing with more effective behaviors; or it can mean adjusting or adding to existing behaviors for better effectiveness. So, content and behavior change are some of the characteristics of a coaching relationship.
Mentoring involves learning at a deeper level which is why it is called "transformational" learning. It means focusing on changing perspective and gaining a greater awareness of self both as a person and as a professional. This type of learning requires analysis of what is happening and how it impacts the mentoree on multiple levels: personal, emotional, professional, etc. So context and the quality of the relationship are some of the characteristics of a mentoring relationship.
Obviously there can be overlaps, but for the sake of clarity and understanding, seeing the learning differences between coaching and mentoring can help ensure that one is in the right relationship based upon the desired outcomes.