Once again I find myself having to explain the difference between these two concepts when actually there can be very little difference in how they're done. Salter and Gannon (2015) suggest there are commonalities to both and that each have different meanings in different contexts.
From my perspective I consider it's worthwhile asking people three questions to decide the activity:-
1. Who decides the aim of the conversation and
2. Who listens to new information?
3. Who asks the key questions?
As a manager or leader (or even collaborator, mentor, coach or teacher) you might be doing a mix of these activities. I'd like to know - how often does the other person know your intentions at any stage, if you merge activities without contracting for your approach? (If rarely, how might that impact your collaborative success?)
Reference:
Salter, T., & Gannon, J. M. (2015). Exploring shared and distinctive aspects of coaching and mentoring approaches through six disciplines. European Journal of Training and Development, 39(5), 373-392.
This article potentially gives an American perspective - coaching is more professional, mentoring more ad hoc https://info.insala.com/coaching-vs-mentoring Although it says coaches do have specific knowledge, the ICF coaching definition clearly implies a coach's job is to encourage the coachee to think, feel, understand and take responsibility. See http://www.icfphiladelphia.org/page-18058
Another readily available article by Tina Salter highlighting the issue is here
http://ijebcm.brookes.ac.uk/documents/special08-paper-01.pdf