Maybe the author definition is from sports, but outside it here is how I see (and how many of people that I encountered so far see) the difference between coach and mentor:
In a coaching relationship the coache sets the agenda not the coach. The coach is more backseat than a mentor. The coach is there to walk along the coachee on the coachee path while providing guidance when asked, usually in the form of guiding questions or helping navigate various points of views or helping go through decision frameworks.
In a mentor relationship the mentor sets the agenda together with the mentee. A mentor has a more active role in the agenda providing active guidance and feedforward. The mentor and the mentee walk together on a path they both agreed on.
As an example:
If I would go to a coach and say ask about should I learn Elixir or not taking into consideration my Ruby background, then the coach will not answer yes or not. But should help me discover for myself the answer. It will usually help me look at this question from various points of view or can provide a decision framework, but the answers (or the content of my answers) will always be mine or my own discovery. So they will not state "Elixir is like Ruby" or "Elixir is not like Ruby" but they might ask "How can you assess if Elixir is like Ruby?" or "What is the smallest project that you can create to see if you like Elixir".
If I would go to a mentor and ask about should I learn Elixir I expect them to tell me pro and cons of Elixir and also have an opinion about if Elixir is really similar with Ruby or not and even express their preference for this programming language or the other.
So I choose to go to a mentor or coach depending on what outcome I want to have and what experience they have.
PS: Please take the Elixir and Ruby just as an example of a technical matter to be discussed with a coach or mentor.