What is the same between Christanity and Judaism?

Answer 1

Considering that Christianity was based on the rejection of Judaism, the two religions don't have much in common. The closest similarity is that the Christian Old Testament is based on the Tanach (Jewish Bible), however, the Christian OT was altered to support the teachings of Christianity.

Both modern religions developed from several different sects of Jewish Temple Religion in response to the Roman destruction of the Temple. They were already widely separated in theology long before this though: the sects that became Christianity believed that the prophesied messiah had come, the sects that became Judaism varied from believing that the messiah had yet to come to there was no messiah at all. There were also many other Jewish religious sects at the same time that have long since disappeared.

The original Christian OT was the Greek Septuagint translation (which was also used by Greek speaking Jews of the time). The text of the Septuagint does more closely agree with Christian theology than the modern Masoretic Hebrew text does (But was translated long before Christianity began). Oddly enough most modern Christian bible translations choose to translate their OT from the Masoretic text not the Septuagint, so the OT that most Christians read today agrees more with the theology of Judaism than with Christianity.