In modern times, since the term rabbi has become commonplace and oft-used, the term rav has come to connote a rabbi with a much greater level of knowledge, wisdom, and understanding in Torah matters, above and beyond what has come to be known as a 'career rabbi' who, for example, conducts significant life events as his salaried job, rather than a person who studies and delves into Torah full-time for no reward or compensation.
In the Talmud, the title Rav generally precedes the names of Babylonian Amoraim, whereas the title Rabbi generally precedes the names of ordained scholars in The Land of Israel (whether Tannaim or Amoraim).
In the Talmud, Rav or Rab (used alone) is a common name for Abba Arika, the first Amora, who established the great yeshiva at Sura, which, using the Mishnah as text, led to the compilation of the Talmud.
From the 16th century and onwards, Rav' or the Rav generally referred to Rabbi Obadiah ben Abraham, a.k.a. haRav miBartenura (the Rav from Bartenura). Rabbi Obadiah miBartenura becomes the Hebrew acronym Rabbi `Obadiah of Bartenura ("?).
More recently, as a sign of great respect, some rabbis are simply called the Rav even outside of their personal followings. Note that when the word is pronounced using a patakh, the meaning is almost universally rabbi Obadiah ben Abraham of Bartenura. When using a kamatz, the term can refer to, among others:
The title Rav HaTzair (or Rav HaTza'ir) refers to an assistant rabbi. Tzair means young, in Hebrew, and the prefix Ha means "the"; the combination can be used to mean the younger of a pair: Rav HaTzair, in context, can refer to the younger of a pair of rabbis, or Junior Rav.
listen to the rav's Shabbos HaGadol drasha
... to feel the rav is looking after them
the Rav Hatza'ir, .. son of the current Rav
Boruch Halberstam, Rav Hatzair of Kiryat Sanz ... last week.
served as Rav hatza'ir under his father's supervision
... his younger brother ... the Rav Hatzair (Junior Rav)