Jewish Christians are the new generation Jews who believed in the Jesus Christ as their Lord. They came from the ancestral lineage of Israel. Non-Jewish Christians are often called gentile Christians. They received the message from the Lord through Jesus Christ and his disciples.
During the early times, there is a demarcation line between the Jews and the Gentiles. Several passages in the Old Testament forbid the Jews from interacting with the gentiles. This has brought cultural differences which apparently led to division and worse disputes and wars. Jews before are not allowed to marry Gentiles or even celebrate with their beliefs.
When Jesus Christ started preaching, the connection of Jews and Non-Jews got better since Jesus emphasized that anyone can be saved through faith in Him. After Jesus' death, his disciples and Paul followers started evangelizing the people with no respecter of religion and race. Paul even preached about the salvation of Gentiles through Jesus Christ.
Today, the relationships of two Christian groups are getting better because of the teachings that Paul has made. There may be some arguments about the customs but that is due to individual and cultural differences.