Proselytize 1: to induce someone to convert to one's faith 2: to recruit someone to join one's party, institution, or cause transitive senses: to recruit or convert especially to a new faith, institution, or cause
Witnessing 1: to bear witness 2: to bear witness to one's religious convictions <opportunity to witness for Christ -- Billy Graham>
I believe the difference in the two is doing the work of man and doing the work of God.
I think there is a subtle difference between proselytizing and witnessing/teaching in that proselytizing involves the use of some type of pressure to persuade the potential convert. The pressure can be quite overt (if you join us we will provide food, shelter, etc...if you don't join us we will kill you) or it can be less obvious (pointing out that non-believers are condemned, making non-members or ex-members social outcasts, etc.). Proselytizing almost always seems to be associated with coersion, judgments and punishments, while witnessing can be quite positive. The best type of witnessing is non-verbal and can't be done in the internet. However, people are often interesting in hearing about someone's own faith journey and that in itself can be a positive form of witnessing. Quoting scripture rarely comes off well, in my opinion. A lot of the best "teachers" are those who would never open their mouth to tell you about their religion/ideology unless you directly asked them. Why would you ask them?
I see it as the difference between being other-centered vs. self-centered in the discussion. Not self-centered as in egotistical, but self-centered as in discussing one's own experience.
Proselytizing is other-centered. One is focused on the condemnation of this other person and converting them, and thus the discussion is about their life, their beliefs, their faults, and their salvation.
Witnessing is self-centered. One is focused on sharing one's own story about experiencing God, one's own beliefs and the reasons for them, one's own faults and salvation. Rather than condemning the other with an eye for conversion, one is focused on sharing one's own testimony with an open mind and heart.
When I have witnessed, I have been invited by another to share my story, and I try to express to them the love, peace, joy, awe that has come from my experience of God, and the changes it has wrought in me. I am not worried about conversion. I trust that God has prepared their heart for finding their own path, and somehow will use my story. I do not see my story as Truth, but rather one person's experience with God, and as such I hope it will be an inspiration to those God has prepared and sent across my path.
From an administrative point of view, the difference is subtle but important -
Someone whose motivation is to insist upon the absolute correctness of their own vision, which much be adhered to, promoted, and advanced, usually at the denigration of other viewpoints.
Can happen in various degrees, from the simple personal affirmation, to full-blown dictation of faith.
The problem arises where one form is exclusive of the interests of the audience, whilst the other is inclusive.
For example, Bobby Winters has a writing column on this site: An Okie in Exile. He is a Christian, whose writings usually center upon a personal Christian approach towards secular issues. This means that he could be construed to be witnessing in some form - heck, some of his pieces are lay sermons, so you could even argue that he's preaching.
However, it is not an approach which derides anybody, attacks opinions or viewpoints that are different, nor dictates that others should take his outlook at their own. He makes a comment on the world, and invites not debate, but discussion and reflection.
This is precisely why I invited him to post writings here - I find them enjoyable, engaging, and often worth reading. Big Buddy is a particular favourite, though there are others.
However, if he simply wrote that he had faith, this was his faith, and that others better take that same faith upon themselves, then he would not be enjoyable or engaging to read, but invasive.
Hopefully that helps with my own personal take on the matter.