Mentoring, internship and training have the same output : Getting knowledge.
The difference only lies with the purpose of this knowledge.
If you search for an internship, you basically want to pass some exam, improve your curricula, and get a diploma and ultimately get a job. The reputation of the company is important to impress future employers and friends. (the business word for it is "credibility")
The downside of internship is that it cost lots of time. It cost money too, because even if you don't pay for it, it steals the time you could use for income.
If you search for training and you are in a company, your goal can be : having a raise, getting fast knowledge on a specific for immediate usage.
If you are not in a company, you are doing it to find a job.
Training are more efficient to acquire knowledge, it is dense, and, if used by practical people, it turns definitively into money. You can even have the benefits from internship with certifications.
The downside is that it cost money, but not so much time. I emphasize that this knowledge should be used for immediate purpose or your brains will forget as fast as he learnt.
If you search for mentoring your purpose is personal development. You want to acquire some parts of the brain of your mentor. The first step is to find this person, and then work with him.
The difference with internship is the purpose : you don't do it for credibility, you do it for your own development. You do it because you want specifically what the mentor has in his head, and you certainely don't want to deal with the brain of anybody else.
Mentoring should be a common practice among employees in the same company. For the mentor, sharing knowledge is awesome. For the mentee, it is the fastest way to not only get the knowledge but to know who you will become.