Most of you may think of a teacher and a coach as the same thing. Personally I feel the two are different in regards to golf. I say this in respect to my career. The first 25 years I played competitive golf as an amateur - The last 25 years as a PGA Professional.
As a PGA Teaching Professional I help players improve their game through better technique. This would include putting, chipping, short game and the full swing. This is the "nuts and bolts" portion helping new players develop sound fundamentals, and build a golf swing that delivers consistent ball flight. We also work with seasoned players who have developed a shot problem such as a slice, poor contact with irons, etc.. This is more the diagnostic and corrective area of instruction.
A coach on the other hand is focusing on playing the game of golf rather than the golf swing. A great coach is usually a person with an abundance of experience and success in playing competitive golf. They help players learn how to play the game. By this I mean how to shoot the lowest possible score regardless of how well they're hitting the ball on a given day. They help a player with the mental challenges of the game such as course management, knowledge of the rules, adverse conditions, dealing with pressure of playing competitively, risk taking and knowing how and what to practice.
For a young aspiring player it is important to have both a teacher and a coach in their corner. As the player's ball striking skills and proficiency improve the more important the mental part of the game becomes. This is where a great coach can be such a big help to the player.