Quick definitions: Coaching, Mentoring, Training
Some links for you below:
Rider Coach: A formal, temporary, paid, position helping an individual achieve certain skills or goals. Defined by goal and task orientation.
Mentor: Informal, usually unpaid, fluid relationship where a person with more experience serves as a role model and possibly sounding board for another less-experience person.
Horse Trainer: Paid position where one improves the responses, skills, patterns and understandings of the horse. (Paving the way for the less experienced-rider.)