International Coach Federation (ICF) defines coaching as partnering with clients in a thought-provoking and creative process that inspires them to maximize their personal and professional potential, which is particularly important in today’s uncertain and complex environment. Coaches honor the client as the expert in his or her life and work and believe every client is creative, resourceful and whole. Standing on this foundation, the coach's responsibility is to:

This process helps clients dramatically improve their outlook on work and life, while improving their leadership skills and unlocking their potential.

(Source is from ICF website: www.coachfederation.org)

Coaching is a partnership, a process of co-creation between the coach and the client.  Here the client is the expert and drive force for his life and work.  So the coach will focus on the client’s agenda, not his own agenda.  

To make it easier to understand, here is the illustration of coaching:

Professional coaching focuses on setting goals, creating outcomes and managing personal change.  It is very helpful to understand what is coaching about and what is coaching not by distinguishing it from other personal or organizational support professions.

Counseling is helping people who have personal or interpersonal issues, which might be pain, dysfunction or conflict. Even through, counselor asks questions, the focus is often on resolving difficulties arising from the past that hamper an individual's emotional functioning in the present, improving overall psychological functioning, and dealing with the present in more emotionally healthy ways. Usually counselor works as an expert to try to help or solve the problems for the clients. Coaching, on the other hand, supports personal and professional growth based on self-initiated change in pursuit of specific actionable outcomes. These outcomes are linked to personal or professional success. Coaching is future focused. While positive feelings/emotions may be a natural outcome of coaching, the primary focus is on creating actionable strategies for achieving specific goals in one's work or personal life. The emphases in a coaching relationship are on action, accountability, and follow through.

Consultant usually function as the know-how person with their expertise on specific areas. They usually diagnose problems facing by the organization and then come up with solution for the clients. Sometimes, they also help to implement the solutions as well.  The time range could be from past to the present and then to future.  With coaching, the assumption is that individuals or teams are capable and resourceful of generating their own solutions, with the coach asking powerful questions, supplying supportive, discovery-based approaches and frameworks.

A mentor is an expert or senior level manager in the organization who provides wisdom and guidance based on his or her own experience with younger employees on one-on-one basis. Mentoring may include advising, counseling and coaching. In corporate world, the purpose of mentoring is to develop high potential talent to the higher level as a career advancement and talent development tool. The mentor usually shares experience and wisdom, helps his/her mentee to enlarge their network, provides exposure to the higher-level management team, and observes and gives feedback to the mentee about what they want to achieve their career advancement. At same time, he/she also evaluates who has the potentials to be promoted to the organization head based on their observation. The coaching process does not include advising or counseling, and focuses instead on individuals or groups setting and reaching their own objectives. 

Training is the instructional process by which specific knowledge and skills are transferred to the trainee based on the current or future needs. Training programs are based on objectives set out by the trainer or top-level management team for specific purposes. They set up their own agenda, not only trainee’s agenda. Some experienced trainer with coaching background might use coaching to facilitate the training, so the trainees get most from it. Training also assumes a linear learning path that coincides with an established curriculum. While coaching is less linear without a pre-set curriculum.

In sports, a coach is a person involved in the direction, instruction and training of the operations of a sports team or of individual sportspeople. A coach may also be a teacher. Though sports metaphors are often used, professional coaching is different from sports coaching. The athletic coach is often seen as an expert who guides and directs the behavior of individuals or teams based on his or her greater experience, knowledge and his agenda. He has the right to decide the game plan and who will be on the field to play. Professional coaches possess these qualities, but their clients determine the direction and hold the agenda. In addition, professional coaching, unlike athletic development, does not focus on behaviors that are being executed poorly or incorrectly. Instead, the focus is on identifying opportunity for development based on individual strengths and capabilities.