Why the Bibles between Catholics and Protestants are different.

This video has other reliable sources and is very informative
It is a brief history of the Bible.
 

'The Missing Books of the Bible' Click to read article

The 7 Books of the Bible that are omitted from Protestant Bibles
Catholics refer to this as "the Deuterocanonical Books"
Protestants refer to them as "the Apocrypha"

Tobit
Judith
1 Maccabees
2 Maccabees
Wisdom
Sirach
Baruch
Also in the Catholic " Deuterocanonical Books" are fuller versions of the Old Testament books of Daniel and Esther.


The colors indicate the sources of these writings everything in [brackets] are the meanings the authors conveyed.

 When was the Old Testament compiled? Some would decide for about the year 430 B.C., under Esdras and Nehemiah, resting upon the authority of the famous Jew, Josephus, who lived immediately after our Lord and who declares that since the death of Ataxerxes, 424 B.C., "No one had dared to add anything to the Jewish Scriptures, to take anything from them, or to make any change in them."

Alexander the Great ended Persian rule at the Battle of Issus (Syria) in 333 B.C. He established Greek rule and cultural influence by setting up a series of military colonies and founding Greek-style cities, the most important being Alexandria (331 B.C.) in Egypt. The Greek language and way of life began to penetrate the eastern Mediterranean world.

...The Jews, in spite of the tenacity of their own religious and cultural traditions, were also affected by this Hellenistic movement, particularly those scattered beyond the confines of Palestine.

... A Greek translation of the Biblical books appeared in Alexandria around 200 B.C. This became known as the Septuagint (from the Latin for 'seventy'), because of the legend that the translation had been done by seventy-two translators, six from each of the twelve tribes. The Septuagint became the Bible of the Jews of the Diaspora (those 'dispersed' in foreign lands). 

  Other authorities, again, contend that it was not till near 100 B.C. that the Old Testament volume was finally closed by the inclusion of the Writings.

 [Whether around 430 BC or 100 BC] one thing at least is certain, that by this last date--that is, for one hundred years before the birth of our Blessed Lord-- the Old Testament [46 books] existed precisely as we have it now.

It was later adopted by Christian missionaries when they took the Gospel into the Hellenistic world of the Roman Empire. The New Testament written in Greek, records 300 of its 350 quotations from the Septuagint version of the Old Testament instead of in direct translation from the Hebrew.

...During the formative days of the Christian Church, the Jews did not possess a formal or explicit canon of the Old Testament books. The Christian writers quoted the broad library of sacred writings used among contemporary Jews. The Jews continued their own discussions about the sacred books, and in the late second or early third century A.D. canonized the shorter collection that Jews and Protestants use today. Modern study by all parties to the current debate have raised questions about the correctness of this late Jewish decision to exclude some of the books which had been accepted as Scripture for more than 200 years.




  The Christians did not establish their Old Testament canon as early as the Jews. 
... The question of the Old Testament canon rested [with 46 books of the OT] during the next 1,000years until it was raised again by the reformers in the sixteenth century. 
  
[Within that 1,000 years] the seven firmly-established Old Testament books were repeatedly declared by numerous early Christian Councils [393, 397,417 A.D. etc...] to be the inspired Word of God, [these] were later deleted from the "Protestant" Old Testament canon decided by Martin Luther and successive Reformers more than eleven centuries later.

 [I]n debating purgatory with J. Maier of Eck (1519), it was Luther who broke with Church tradition and began a new era in discussions on the Old Testament canon... Confronted by 2 Macc 12:46 as 'scriptural proof' for the doctrine of purgatory, Luther rejected 2 Macc as Scripture.
             The early reformers were not eager to reject the ...[deuterocanonical books] altogether, since they had been in ecclesiastical use for more than a millenium.

 In his translation of 1534, Martin Luther grouped the deuterocanonical books together at the end of the Old Testament as books which 'are not held equal to the sacred scriptures and yet are useful and good for reading.' The Reformers, in deciding to get back to the situation at the time of the Church's origin, wanted to adopt as scripture the books that made up the Old Testament used by the early Christians. They presumed that the books revered by the Jews of their own time had always been the canonical Old Testament, and so the shorter list of books became the Old Testament of the Reformers. They did not know that the decision for a shorter Old Testament canon had been late in coming, and that during the first century both Jews and Christians held a wider selection of Old Testament books. In reaction to the Reformers, the Council of Trent in 1546 [formally] defined the longer Old Testament canon as inspired scripture."
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Special thanks to the book:
Unabridged Christianity
By Fr. Mario Romero
Where the green and yellow sources came from

The Catholic Bible Study Handbook
by
Jerome Kodell, O.S.B. 

Where We Got the Bible: Our debt to the Catholic Church
by
Henry G. Graham

The New Jerome Biblical Commentary
(editors) Raymond Brown, Joseph Fitzmyer, and Roland Murphy 

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What Are good Catholic Bibles?