There may be a strict definition, but in my experience, your teacher is your regular instructor with whom you, or you and your partner practice regularly vs. a coach is someone the studio brings in on a sporadic basis (often world-class) to elevate your technique, or help with choreography, or just bring a fresh and different perspective to your dancing. If you are just starting out, the coach will work with you and your teacher together. Coaches are usually prior chmpions who are now judging and teaching (and travelling extensively...therefore not affiliated with any one studio). If you are serious about competetive dancing, it's worth finding a studio that attracts these coaches on a regular basis.