Update: 2017.10.29
Prior to the 5th century CE, Rav was used as the title specifying a particular Diaspora (Babylonian Reform) Âmor•âꞋ (e.g., "One day, Rav went…," or "a servant in Rav's house…" and the like), Rav refers to the leading Babylonian Reform Âmor•âꞋ, a tal•midꞋ who received sᵊmikh•âhꞋ from Yᵊhud•âhꞋ ha-Nâ•siꞋ in Yᵊhud•âhꞋ, founder of the academy at Sura (c 220 CE), and credited with being a co-founder in the compilation of the Tal•mudꞋ Ba•vᵊl•iꞋ: àÇáÌÈà áÌÇø àÄéáÌåÉ (175-247 CE).
In its 5th century CE mishnaic (i.e., Talmudic) Hebrew sense, Rav was an exclusively Diaspora (Babylonian Reform) title recognizing one's "greater" (more popularly expressed in American English as "one's better"), from which it has popularly, but inaccurately, been rendered as "master."
While most rabbis encourage the historically anachronistic misassumption that rabbis were present with Mosh•ëhꞋ at Har Sin•aiꞋ, the historical reality is that there were no rabbis until the formation of the Pᵊrush•imꞋ party, which splintered off from the Tzᵊdoq•imꞋ between B.C.E. 134-104 under the rule of Yokhâ•nânꞋ Hyrcanus (nephew of YᵊhudꞋâh Ma•kab•iꞋ (b. B.C.E. 164, Ko•heinꞋ ha-Jâ•dolꞋ B.C.E. 134, d. B.C.E. 104).
Rav is the title of a post-135 C.E. Pᵊrush•iꞋ Tor•âhꞋ interpreter and expounder of Tor•âhꞋ and Ha•lâkh•âhꞋ – the "Sage," who invariably earned his living from a non-religious occupation like everyone else and who had met the required standards and obtained legitimate recognition of receiving sᵊmikh•âhꞋ.
"In [Yᵊhud•âhꞋ], the custom [that] had been instituted during the [period of the Tanâ•imꞋ], of according the title [RibꞋi] to scholars ordained by the Nâ•siꞋ and [Beit-Din ha-Jâ•dolꞋ], continued [though, after 135 CE, conferring only the lesser title of Rav] during the period of the Âmor•âꞋyim" ("Amoraim," EJ, 2:873).
As the title of Rav (corrupted in modern Hebrew to "Rabbi") became more widely known after 135 C.E., the distinction from, and even awareness of, the title of RibꞋi was lost to all but a few of the most historically knowledgeable Jews.
RabꞋi ("Rabbi", by contrast, is anachronistic relative to Yᵊhud•âhꞋ in the first century C.E.. The following is excerpted from note 23.7.1 of The Nᵊtzâr•imꞋ Reconstruction of Hebrew Ma•ti•tᵊyâhꞋu (NHM, in English).
The term for 1st century and earlier Pᵊrush•imꞋ Kha•khâm•imꞋ like Hi•leilꞋ, Sham•aiꞋ and Ja•mᵊl•iy•eilꞋ, is RibꞋi ("Titles," Ency. Jud., 15:1163-4). This group includes the most famous RibꞋi of all time, upon whom Ja•mᵊl•iy•eilꞋ himself conferred sᵊmikh•âhꞋ—RibꞋi Yᵊho•shuꞋa Bën-Dâ•widꞋ, ha-Mâ•shiꞋakh.
Though anachronistic in the 1st century CE, by the 3rd century CE, the terms RabꞋi and Rav had, in that order, both come into popular, including Hellenist, usage and the distinction between them was, by then, becoming increasingly, blurred.
In its 5th century C.E. mishnaic (i.e., Talmudic) Hebrew sense, Rav is exclusively a Diaspora (Babylonian) title recognizing one's "greater" (more popularly expressed in American English as "one's better"), from which it has popularly, but inaccurately, been rendered as "master."
In Tal•mudꞋ, both RabꞋi and Rav are sometimes used alone to refer to two specific Kha•khâm•imꞋ. Prior to > century CE, Rav was used as the title specifying a particular Diaspora (Babylonian) Âmor•âꞋ (e.g., "One day, Rav went…," or "a servant in Rav's house…" and the like), Rav refers to the leading Babylonian Âmor•âꞋ, a tal•midꞋ who received sᵊmikh•âhꞋ from Yᵊhud•âhꞋ ha-Nâ•siꞋ in Yᵊhud•âhꞋ, founder of the academy at Sura (ca. 220 CE), and credited with being a co-founder in the compilation of the Tal•mudꞋ Ba•vᵊl•iꞋ: àÇáÌÈà áÌÇø àÄéáÌåÉ (175-247 CE).
Rav must be distinguished from RabꞋi (Anglicized to "Rabbi"), which refers to Yᵊhud•âhꞋ ha quasi-Nâ•siꞋ (135-220 CE.) Notice, too, that, by 135 CE, even sᵊmikh•âhꞋ conferred in Yᵊhud•âhꞋ, and by the quasi-Nâ•siꞋ, merits only the lesser title of Rav (in contrast to the pre-70 CE title of RibꞋi).
øÄáÌåÉï, is used of é--ä, most popularly in the phrase øÄáÌåÉðåÉ ùÑÆì òåÉìÈí (Rib•on•oꞋ shël o•lâmꞋ; Sovereign-Great of the world-age). See also a•don•iꞋ and morꞋi.