Word Distinction: Passing on Knowledge

Teach is the general word for helping a person or group of people to learn something.
If you instruct a person or group of people you pass on knowledge to them but you cannot be sure that they have learnt anything:
He instructed us in Latin, but some of us made little progress.
You can train a person or group of people up to a necessary level in a particular skill or profession, and you can even train an animal:
It takes several years to train a doctor.
to train a dog to do tricks
You can coach a person or group of people, often outside the educational system, such as in sports, and often for a particular examination which they find difficult and which they must pass: Because he failed the chemistry examination at school, he had to be coached in chemistry at a private educational institution.