First, we must realize that our modern Bibles differ in many small details from the Scriptures that were available to the earliest Christians. The earliest manuscripts of the Hebrew Bible on which most of our modern Old Testaments are based date to about AD 900, but before that time many copies of the Hebrew Bible had slight differences. The New Testament writers had access to these earlier versions of the biblical books, and it is those versions that they quote – meaning that their quotations often have slightly different wording from the same verses in our modern Bibles.
Next, we should be aware that not all the New Testament writers knew Hebrew. For example, Luke, the author of the third Gospel and the book of Acts – and evidently a speaker of Greek – may not have known the Hebrew language. He seems to frequently quote from the Septuagint, a translation of the Hebrew Bible into Greek that was made in the third and second centuries BC. The author of the book of Hebrews certainly was also more comfortable using Greek and never quotes directly from the Hebrew Bible – only from the Septuagint and other versions. And even the apostle Paul, though he clearly knew Hebrew, also used the Septuagint at times. In fact, of the approximately 300 Old Testament quotes in the New Testament, approximately two-thirds of them came from that Greek translation, and these quotes often differ very slightly from the wording of the Hebrew Bible. The New Testament writers evidently had no difficulty in regarding such translations as the Word of God.
Also, we don’t think it strange today when Christian teachers or preachers quote a specific translation in order to best make the point they are trying to get across. Sometimes a given translation uses the exact word that is being discussed – for example, confidence instead of faith – so a particular modern-day translation of the Bible may work best in a given message or under particular circumstances. The New Testament writers were no different and seem to have sometimes chosen a version of the Bible that provided wording that best fit their message.
Another thing to keep in mind is that today we can easily access a Bible in order to quote a particular verse, but few early Christians owned complete copies or even parts of the Scriptures. The New Testament writers often had to rely on memory in order to include the gist of a biblical verse or passage in their own writing. Writers like the apostle Paul (who quotes the Old Testament some 183 times in his epistles) knew the Scriptures well enough to be able to quote them exactly or close to exactly from memory.
Finally, the writers of the New Testament sometimes combined two or more verses from the Hebrew Bible in order to make their point. This is no different from today when we quote from several pages of a book or even from several sources in our own writing. But first century writers did not utilize footnotes or other forms of citation (which appeared much later in history) to note exactly where each quotation came from. For example, in his epistles, Paul sometimes introduced quotations from the Old Testament by saying something like “it is written in the law” (1 Corinthians 9:9; etc.). But at other times he simply made the quotation without even mentioning where it is from when he was confident that his readers would recognize the verse (Romans 2:24; etc.) Even if verses from different areas of the Scriptures were quoted together, when the New Testament writers knew they were writing to individuals who knew the Scriptures well, they simply quoted the verses without mentioning where they were from.
An aspect of this topic that can be helpful in our own study of the Bible is that it often pays to compare a New Testament quotation with its original verse in the Old Testament (which is usually cited in the footnotes of modern translations). This is not because we need worry about minor differences in wording, but because looking at the context in which the Old Testament verse appears can often help us more fully understand the New Testament reference. The New Testament writers knew that many of their readers would not only recognize the verses they quoted, but also would know the setting in which they appeared.