There is a judo version of this question about the difference between a sensei (mentor) and coach (cornerman). The United States Judo Federation has a long answer to this question that considers the cultural history and etymology of these words, what functions they perform, and how the roles may overlap, but basically comes to the conclusion that the difference is about winning in sports. The concept of a coach or cornerman is sport-based, while other terms for instructors are not.
If you are basically interested in sport, find an instructor who specializes in sport (a coach or cornerman). If you have interests beyond sport (learning to teach, health, life advice, etc.), find an instructor who does not focus exclusively on sport. Winning in sport is a specialization with its own skill set.
In reality, you have to choose from among the instructors you have available, and the spectrum of available skills and strengths does not separate into neat categories. As with any relationship, you have to work out with the other party what the parameters of yours will be.