What if the proselytizer is willing to listen and be proselytized, even as he tries to proselytize?
In other words, what is the difference between debate and proselytizing?
It depends on the debate.
A debate is a forum where opposing ideas are presented, and it can serve many different purposes. Proselytizing is the activity of attempting to convert people to your ideology.
If you use debate to achieve that goal, then it is proselytizing. If your goal is something else, then it is not proselytizing.