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The basic difference is the number of books that are considered to be inspired by God and admitted to the Canon.
The Catechism of the Catholic Church of 1994 stated, "The Church accepts and venerates as inspired the 46 books of the Old Testament and 27 books of the New” (# 138).
The Protestants for the most part recognise just 39 books of the Old Testament and 27 books of the New to be inspired.
7 of the Old Testament books were not considered by the Jews to be inspired by God. The books are Tobit, Judith, 1 Maccabees, 2 Maccabees, Wisdom (of Solomon), Sirach, and Baruch. Parts of existing books were also removed including Psalm 151 (from Psalms), parts of the Book of Esther, Susanna (from Daniel as chapter 13), and Bel and the Dragon (from Daniel as chapter 14).
The 7 books are classed as Second (Deutero) Canonical by the Catholic Church (which Catholics assure us does not mean second-class) and included in its Bibles. The books are called by Protestants Apocrypha (from the Greek - meaning ‘hidden away’) and not considered to be inspired. ‘Apocrypha’ has changed its meaning over time to that of being false, spurious, bad, or heretical.
Jerome (c. AD347) considered the 7 Deutero-Canonical books to be NOT inspired by God, but he was commissioned by ‘Pope’ Damasus to translate all 73 books into Latin. Damasus considered the 7 books to be inspired by God.
To my mind the difference between the Apocrypha and the inspired books of the Bible is marked and self evident but because some of the false doctrine of the Catholic Church has its support in the Apocrypha, one can see why the Church has to retain it. The Apocrypha supports such nonsense as: Prayers for the dead (Tobit 12:12; 2 Maccabees 12:39-45): Purgatory (Wisdom 3:1-7): Intercession of saints in heaven (2 Maccabees 15:14): Intercession of angels (Tobit 12:12-15).
Another difference is the translation of the Greek word ‘metanoeo’ (which literally means ‘think again’) with the words ‘do penance’
NKJV Matthew 3:2 and saying, "Repent , for the kingdom of heaven is at hand!"
Douay-Rheims Matthew 3:2 And saying: Do penance : for the kingdom of heaven is at hand.
We can see at once the difference that this makes to doctrine.
If you want to check for other differences, a King James translation can be viewed alongside a Douay-Rheims at most ‘parallel Bible’ websites such as www.biblegateway.com
I hope this helps.