A mentor is someone who provides for support, advice, counsel and the dissemination of their experience and wisdom. They do not set out to teach and certainly not to train.
A mentor is responsive to the person they are mentoring; there might be regular sessions but the direction and content of the exchange is largely driven by the needs of the person being mentored. A mentor who tries to direct the end result of any learning process is overstepping their boundary; this happens a lot with Dom-sub mentoring simply because a dominant will naturally want to control the end result.
The word mentor is from a character in Homer's Odyssey; he was a trusted advisor and counsellor. This is what a mentor is, still. The word has no connection with monitor.