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.)
Split of Christianity and Judaism
Most of Jesus's teachings were intelligible and acceptable in terms of Second Temple Judaism; what set Christians apart from Jews was their faith in Christ as the resurrected messiah. While Christianity acknowledges only one ultimate Messiah, Judaism can be said to hold to a concept of multiple messiahs. The two most relevant are the Messiah ben Joseph and the traditional Messiah ben David. Some scholars have argued that the idea of two messiahs, one suffering and the second fulfilling the traditional messianic role, was normative to ancient Judaism, predating Jesus. Jesus would have been viewed by many as one or both.