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.)