The difference between a Trainer and a Coach, and why you need both

After coaching for several years and getting coached for some time too, I have come to the realization that in chess there is some distinction between the terms "trainer" and "coach."

If you are thinking that they are the same thing, then you are already skipping to the conclusion of this post, but for the purpose of this discussion we point out the perceived distinctions:

A Trainer "trains" and a Coach "coaches." More specifically:

Trainer: provides carefully picked training problems for the student to solve, typically tailored to teach a lesson or address the student's weakness

Coach: Provide guidance on training methods tailored based on analysis of the student's games. 

If you already have a coach, then you may notice that your coach already does these things from both categories, or maybe even that they do not.

I purposely am using only the word "coach" because in the common chess world, we tend to hire "coaches." (I should note that "trainers" definitely do exist as a true separate entity especially for top GM's)

This means the following:

A Coach must also fulfill the role of a trainer.

This is an important realization that would help both parties:

For students: you should expect your coach to do both training as well as guidance (how should you be training? how often should you play? any of those kind of general questions)

For coaches: If you want to keep your students, you must make sure you do both as well.

Of course as stated before, you could respect the distinction as well, but I emphasize again that this distinction is ambiguiated when talking about amateur chess (99% of the public)

I realize that I am perhaps less experienced than many coaches/students, but these are my viewpoints and I feel that they are general enough to hold at least some truth.

Thank you, and good luck!