In sports, what is the difference between a coach and a trainer?

Recently I seen in my gym in basketball court "Rules for Coaches and Trainers..." What is the difference between Coaches and Trainers in sport context? Why they specifically named separately in the rules?

here it's interesting topic regarding link between train and coach to transportation context Are the dual transportation and learning meanings of both "coach" and "train" just a coincidence?

Broadly speaking, a coach is someone who is in charge of the entire team's preparation, while a trainer's job is to focus on individual athletes' conditioning.

Linguistically ... uh ... etymologically ... the two words come from two different sources, even though they mean, roughly, the same thing.

Train, a verb meaning instruct, discipline, or teach was first recorded in the 16th Century. It comes from the Old French train, which means "to pull, draw," which, in turn, comes from from the Vulgar Latin traginare.

Coach comes from the Hungarian kocsi szekér, a wagon of Kocs, village in Hungary where coaches were first made. The habit of calling a teacher coach may have come from the idea that the instructor carries his pupils. The origin of the term is traced to 19th Century Oxford slang.

If this is in America, then the difference is that a "Coach" is the person responsible for the on-field training, tactics, technique, management, games, etc. A "Trainer", in America, is an "Athletic Trainer", who is responsible for the health and safety of the players, sort of like a Physio in Professional football in Europe.