Judaism
Around the 1st century CE, there were several small Jewish sects: the Pharisees, Sadducees, Zealots, Essenes, and Christians. After the destruction of the Second Temple in 70 CE, these sects vanished. Christianity survived, but by breaking with Judaism and becoming a separate religion; the Pharisees survived but in the form of Rabbinic Judaism (today, known simply as "Judaism"). The Sadducees rejected the divine inspiration of the Prophets and the Writings, relying only on the Torah as divinely inspired. Consequently, a number of other core tenets of the Pharisees' belief system (which became the basis for modern Judaism), were also dismissed by the Sadducees. (The Samaritans practiced a similar religion, which is traditionally considered separate from Judaism.)
Jews
Without a Temple, Greek-speaking Jews no longer looked to Jerusalem in the way they had before. Judaism separated into a linguistically Greek and a Hebrew / Aramaic sphere. The theology and religious texts of each community were distinctively different. Hellenized Judaism never developed yeshivas to study the Oral Law. Rabbinic Judaism (centered in the Land of Israel and Babylon) almost entirely ignores the Hellenized Diaspora in its writings. Hellenized Judaism eventually disappeared as its practitioners assimilated into Greco-Roman culture, leaving a strong Rabbinic eastern Diaspora with large centers of learning in Babylon.