While biblical infallibility claims that the Bible is without error in every matter required for salvation, Biblical inerrancy claims that the Bible is without error in every detail possible, including scientific and historical details.
The distinction between Biblical infallibility and Biblical inerrancy matters because many people, when first confronted with the apparent contradictions in the Gospels, stop believing in central doctrines like the virgin birth and physical resurrection of Jesus.
Another way of describing this distinction is that the Bible is inerrant in a limited sense, on matters of doctrine and practice, rather than in an unlimited sense, on every possible historical and scientific detail. The Bible, like Jesus, is fully divine and fully human.
To insist upon unlimited inerrancy seems like docetism, ignoring the element of human authorship. We have four Gospels specifically to give us four uniquely human, though divinely inspired, perspectives.
When assessing ancient documents by normal historical standards, their reliability isn't determined by exactness in every possible detail. For example, Jesus most likely cleansed the temple near the end of His ministry, like in the synoptic Gospels, rather than in the beginning, like in John.
This would explain why the Jewish authorities were provoked to execute Him. John, on the other hand, placed it in the beginning, in order to establish Jesus' authority over the temple as the Son of God, since the primary emphasis of John's Gospel is the deity of Christ.
This is only a problem if one insists that the Bible is inerrant word-for-word, rather than in doctrine and practice:
Those who hold to unlimited inerrancy insist that the Bible is inerrant in every possible detail, while those who hold to limited inerrancy, also known as Biblical infallibility, regard the Bible as inerrant in matters of doctrine and practice.
It's simply an unprovable assumption that the Gospel authors intended for the events described to be placed in a strictly chronological, rather than thematic, order.
While every historian agrees that Hannibal crossed the alps to Rome, the ancient accounts contradict each other on which road led him there:
While every historian agrees that Hannibal crossed the alps to Rome, the ancient accounts contradict each other on which road led him there, just as the Gospels contradict each other on minor details like how many angels were at the tomb, while agreeing on Jesus' physical resurrection.
This same point is made in Lee Strobel's The Case for Christ, one of the best-selling evangelical titles in the last twenty years. There is a historical difference between evangelicalism and fundamentalism, and the scholars interviewed in Lee Strobel's The Case for Christ, including William Lane Craig, would be considered evangelical, but not fundamentalist.
In traditional Jewish commentaries, the Book of Job might be entirely allegorical, rather than a historical account. This is only a problem if the Bible is seen as inerrant word-for-word, rather than in doctrine and practice:
That the Book of Job might be an allegorical theodicy doesn't give us license to interpret Jesus' virgin birth and physical resurrection allegorically, because these truths are essential to historic Christian faith, just as the giving of the Commandments on Sinai is central to Judaism.
Those who believe in limited inerrancy have a higher view of scripture than Martin Luther did:
Those who insist upon unlimited inerrancy miss the point as to why the scriptures were written in the first place, "to make you wise for salvation through faith which is in Christ Jesus," to instruct in righteousness, to equip for every good work, and to correct false doctrine, none of which requires that the Bible be word-for-word inerrant on every possible historical and scientific detail.
2 Timothy 3:15-17
and that from childhood you have known the Holy Scriptures, which are able to make you wise for salvation through faith which is in Christ Jesus.
All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work.
If unlimited inerrancy were true, then the mustard seed would be the smallest of all seeds, which it obviously isn't. Jesus' point was to illustrate the power of faith, even if the size of a mustard seed, rather than teach botany. Matthew 13:31-32