Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
A detailed and informative answer can be found by consulting Jewish and Christian sources. This is not our specialty.
In principle both the Jews and Christians are people of the children of
Allah Says (interpretation of meaning): {Verily, We did send down the Taurât (Torah) [to Mûsa (Moses)], therein was guidance and light, by which the Prophets, who submitted themselves to Allâh's Will, judged the Jews. And the rabbis and the priests [too judged the Jews by the Taurât (Torah) after those Prophets] for to them was entrusted the protection of Allâh's Book, …}[5:44].
Then Allah Sent Jesus (Alaihi Salaam) to refresh the Shariah of Moses (Alaihi Salaam) and to correct the distortions, falsifications and mistakes that have been committed by the Jews. The group of the children of
The evidence of the origin of the Christians being from the children of
Anyway both the Jews and Christians are from the children of
However, there are a lot of differences between them nowadays, but they are both misguided and have deviated from the truth and correct methodology.
For more information about them, please refer to religious books on this subject.
Allah knows best.