Physical Skills are needed for sport and they are not necessarily given to you by your coaches. A coach will not give you strength, agility, endurance, stamina, flexibility, etc. Coaches can certainly help you improve these physical skills/attributes. Most importantly, a coach will help you to utilize these skills in order to best participate in your sport, achieve your goals, and work towards higher levels of performance.
Mental Skills are needed for sport and they are not necessarily even addressed by your coaches. A coach will not give you imagery, self-talk, awareness, relaxation, goal setting, etc. Coaches can sometimes help you with motivation, confidence, and/or team cohesion – but this may be inadvertent or indirect. A sport psychologist can help you improve these mental skills/attributes. Most importantly, a mental skills coach/sport psychologist will help you to become more aware of your strengths and limitations with these skills. They can help you to learn how to sharpen these skills and enhance your mental ability to perform at your optimal level. Most elite athletes will tell you that at the highest level, the physical skills will become less relevant because everyone will have them in spades. They will likely tell you that the one thing that will separate you from the masters to the elite is the mental skills and mental edge.