In the name of GOD, Most Gracious, Most Merciful!
The phrase "People of the Book" refers to the receivers of the Torah and the Injeel. To me, this term does not include the receivers of the Quran. The confirmation of this meaning is found in the following verse:
Say, "O People of the Book, you have nothing to stand on until you uphold the Torah, and the Injeel, and what was brought down to you from your Lord." 5:68
The words in 5:68 make a clear link between the "people of the Book" and the receivers of the Torah and the Injeel.
In contrast, the phrase "those who were given the Scripture" refers to all people who received a Scripture from God. This phrase, therefore, includes the ones who received the Torah and the Injeel, as well as those who received a Scripture before the Torah and also the receivers of the Scripture revealed after the Injeel, which is the Quran. The confirmation of this meaning is found in Sura 6.
If we read verses 83 up to 86 we read a long list of prophets "Abraham, Isaac, Jacob, Noah, David, Solomon, Job, Joseph, Moses, Aaron, Zachariah, John, Jesus, Elijah, Ishmael, Elisha, Jonah, Lot".
Following the list of prophets above, we read the following:
Those are the ones to whom We have given the Scripture, the law, and the prophethood. If they disbelieve in it, We have entrusted it to a people who are not disbelievers therein. 6:89
Verse 89 tells us that all the prophets listed were "given the Scripture". This confirms that the term "those who were given the Scripture" includes all who received a Scripture from God. We know for example that Abraham lived before the revelation of the Torah and the Injeel, and that he was given a Scripture from God (87:19). The same applies to all other prophets including Prophet Muhammad, the seal of all prophets.