Not really, but that doesn't make one good and the other bad.
There's certainly an element of mentoring in discipleship, but with a profound and unavoidable difference: Jesus did not say, "Go and make mentees." If He had wanted us to make "mentees" he could have said so. But He didn't. Rather, He said, "Go and make disciples."
Jesus isn't looking for mentors to teach life lessons. He's looking for disciple-makers to teach others how to follow Him. Both mentoring and discipleship are powerful concepts. We need both. Don't throw the baby out with the bathwater. Let's just make sure we understand the difference. So what's the difference?
Mentees follow their mentor, but disciples follow Jesus. That's a huge difference. The Corinthians got caught up in following mentors, and it created embarrassing divisions. Paul even said it made them look like spiritual babies--still worldly. He said, "For when one says, 'I follow Paul,' and another, 'I follow Apollos,' are you not being merely human? What, after all, is Apollos? And what is Paul? Only servants, through whom you came to believe.... For no one can lay any foundation other than the one already laid, which is Jesus Christ" (1 Corinthians 3:4, 11)
It's probably okay, for comparison and clarification, to say, "Discipleship is 'spiritual' mentoring." Or to say, "Mentoring is discipleship without the spiritual side." However, why not just use the word Jesus used: discipleship? In this case, old is gold.