It depends on the context of the position. At the gym, a trainer helps you use proper form. A sports team is run by a coach. A sports team might also have a few trainers to help the athletes perform better. Outside of physical fitness, a coach might act as a guide or supporter; someone to bounce ideas off of. A trainer might be someone who imparts more specific, technical knowledge. A trainer teaches you how to do something, while a coach helps you achieve your goals.

i'm not sure, but may be trainer is for those who are more evocated to the tactial part of a team, and trainer with the training. In soccer and in spanish you will find that diference betwen "director tecnico" (that word by word translation: "technical director") and entrenador (trainer)