Almost every institutional division in Judaism since 1800 traces to this question, and it is more consequential than any dispute about the existence or nature of God.
Orthodox and Haredi Judaism holds the revelation at Sinai as historical and the text as of divine origin, and therefore holds the commandments to be binding without remainder. Change happens through interpretation within the halakhic system, and the system is not open to revision from outside on historical grounds.
Conservative Judaism, descending from the positive-historical school of Zacharias Frankel, affirms that Judaism rests on revelation while accepting that the texts have a history and that the tradition developed. It teaches the critical scholarship in its seminaries and continues to legislate through halakha, which its critics on both sides regard as unstable and which it regards as the only honest option.
Reform Judaism treats the Torah as the record of Israel's encounter with God rather than as dictation, which is exactly why it can regard ceremonial and ritual law as non-binding while holding the ethical and prophetic content to be the enduring core.
Reconstructionism reframes the whole question, taking Judaism as the evolving civilisation of a people, so that the authority of a practice lies in its function within that civilisation rather than in a revelatory event.
Karaite Judaism, a thousand years older than any of these, accepts the written revelation in the strong sense and denies the oral Torah, which produces observance visibly unlike rabbinic practice.
The comparison with Christian arguments over biblical inerrancy is close in structure and different in stakes. In Christianity the question bears principally on doctrine; in Judaism it bears principally on practice, on whether one may drive on the Sabbath, who counts as a Jew, and who may be ordained. That is why the arguments have been sharper and the institutional separations cleaner.