This claim is not true simply because the Prophet salla Allahu alaihi wa sallam was illiterate and didn’t read or write. He also didn’t hear or meet Christians to learn from them.

The stories in principle are the same because these are the Messengers of Allah and the Quran is a revelation from Allah.

There are a number of differences between the Quran and the Bible as you don’t read any of the unaccepted stories about Messengers committing incest or fabricated nonsense as in the case of a human beating Allah in a fight.

The details of Yusuf’s story peace be upon him in the Quran resembles nothing in the Bible and also the true nature of Jesus peace be upon him in the Quran is nothing like the story of Crucifixion.