The main difference between the contemporary and traditional versions of "The Lord's Prayer" is a change of the last sentence. The traditional form derives from the Gospel of Mathew 6:9-13. The contemporary form first appeared in the Anglican Church's Book of Common Prayer from 1662 CE.
The last line in the traditional form reads: "For thine is the kingdom, the power and the glory, forever and ever. Amen." The last line in the contemporary version is: "For the kingdom, the power, and the glory are yours now and for ever. Amen."
A few Anglican Churches still use the King James Version of the Book of Common Prayer, which has the traditional language. To confuse the issue even further, the Roman Catholic Church eliminates the last sentence. The Catholic version of the Lord's Prayer ends with: "And lead us not into temptation, but deliver us from evil. Amen."
The use of the Lord's Prayer without the last sentence goes back to the early days of the Catholic Church. The last sentence was not found in the Biblical references, so it wasn't added by Rome. Church goers in the eastern part of the Roman Empire first added the sentence as a doxology. This is a hymn-like ending to a prayer that honors God.
When the Eastern Orthodox Church broke away from Rome, they deleted the last sentence. But, when the Protestants broke away, they added it.