The Subject: line is the question. I’ve heard Jewish clergy, for lack of a better word, referred to as both rabbis and rebbes. The only difference I’ve seen is that those identified as rebbes are always elderly, and always have beards; Orthodox or Hasidim, perhaps.
So … is there a difference between a rabbi and a rebbe?
Rebbe is just a Yiddish version of the word “Rabbi”. The Hasidim use it to refer to their Rabbis. Also, don’t confuse Rebbe with Reb, which is a Yiddish title of respect.
Even in the non-Hasidic Orthodox world, “Rebbe” is sometimes used in place of “teacher” in the case of a Rabbi who primarily works in a school rather than in a community setting. (This usage is mostly for teachers of Talmud.) But you’re most likely to have heard the term in the sense that Captain Amazing uses it, as the chief rabbi of a Hasidic sect.