I'm not sure of the difference, I'll leave it to an native speaker. But the root of معلم is ع ل م or 3-L-M, which has a basic meaning of "know" or "knowledge". Mu3allim / معلم means a person who causes someone else to know, so, a teacher. The mu- is actually a prefix that goes with this form.

I was curious about the same question and found this answer. I can’t comment on whether or not it’s correct, but it sounds convincing to me.