Coaching and mentoring: what's the difference?

Ask this question and you will get a different answer from each person who gives you an answer. How can this be?
There is much talk in the workplace about both of these disciplines yet no consensus; therefore this post is not to define them but to offer my understanding/application/and personal definitions.

Mentoring, to me, is something a senior worker offers a junior worker.
Many years ago as I was leaving a post I was tasked with mentoring my replacement for a few weeks so that they could step in to the role fully upon my departure.
I have recently worked with a client who was formally asked to mentor a new hire - ensuring he understood the software, projects, hierarchy of tasks and other parameters of his new post.
Mentors offer support and guidance and advice. They will help you learn your job or specific tasks better. They often act as a role model.
I see mentors as being experts in specific skills related to performance, being experienced in an area with established networks.

So what is coaching? (For clarification I am discussing business or executive coaching.)
Coaching is about increasing performance, improving soft skills, and upping efficiency.
A coach is an expert listener and questioner but may not be an expert in a specific field or task: as a mentor often is. A coach should be an expert in adult learning, communication, motivation, psychology/human dynamics and generally understanding what makes a person tick.
Coaching will include self-evaluation and self-discovery. Guided, yes, but not so much directed.
A coach will have a targeted outcome related to optimization of potential.
In a coaching relationship the 'answers' should come from the client whereas in mentoring the mentor will usually provide the 'answers'.

These definitions were provided on another forum:
Coaching is a facilitated, reflective learning process involving semi-structured, focused interaction with an individual (or group) aimed at promoting sustainable change for the benefit of the individual and potentially other stakeholders.

Mentoring is a method of guidance whereby one person shares their knowledge, skills and experience to assist another to make progress in their own lives and careers.

I think those are excellent functional definitions that match my practical understanding of mentoring and coaching.

I would love to hear more about your understanding and applications of these techniques and what you think about what I've said.