What are the different forms of adressing someone who is a Rav, A Rebbe, a HaRav. And why?
The different forms of addressing rabbinic figures are expressions of respect, and do not possess a great deal of significance beyond that.
The titile Rav or Rabbi is traditionally reserved for those who possess semichah (rabbinical ordination); in the Gemara, Shmuel is not termed Rav Shmuel, because he did not receive ordination.
However, today, the term is used very loosely, and anybody who has a solid Torah background, and is fairly erudite in Torah matters, will be referred to by some as Rav So-and-so.
‘Rabbi’ is a little more formal, and will usually refer to somebody with ordination. Ha-Rav is used as a form of extra respect for somebody on a higher level of Torah study and knowledge that the regular Rav.
The term Rebbe sometimes refers to a Chasidic Rebbe (the leader of a Hasidic sect), but is also used in reference to a close mentor, or to a teacher in a Torah school (cheider).