Quotes are taken from J. I. Packer‘s article entitled Infallibility and Inerrancy of the Bible adapted from: Ferguson, Sinclair B. and David F. Wright, New Dictionary of Theology, (Downers Grove, IL: InterVarsity Press) 2000, c1988. The words and sentences in italics are my own notes.
Infallibility signifies the full trustworthiness of a guide that is not deceived and does not deceive. The Westminster Confession (1647) spoke of the Bible’s ‘infallible truth’, the Belgic Confession (1561) called it an ‘infallible’ rule (see Confessions), and Wyclif (1380) named it the ‘infallible rule of truth’.
Inerrancy signifies the total truthfulness of a source of information that contains no mistakes; the word is 19th-century, but the belief it expresses is as old as Christianity. Clement of Rome (90–100) held that in ‘the Holy Scriptures which are given through the Holy Spirit … nothing iniquitous or falsified is written’, and Augustine declared: ‘I believe most firmly that none of these (canonical) authors has erred in any respect of writing.’ Christian belief in the normative authority of Scripture rested from the start on confidence that all Scripture is God’s true teaching through the human writers.
(this seems to be the expansion of implication derived from above. If a certain thing/person is trustworthy, thus, to raise the bar on being able to put full dependence in that trustworthiness; “Is the source of trustworthiness contain no error?” Inerrancy seems more of a reaction to questions that undermine the trustworthiness of scripture.)
Some evangelicals who affirm that Scripture is infallible, never misinforming or misleading us, will not call it inerrant because they think that word tainted by association. They see it as committing its users to: 1. rationalistic apologetics that seek to base trust in the Bible on proof of its truth rather than on divine testimony to it; 2. a docetic view of Scripture that obscures its humanity; 3. unscholarly exegesis that lacks semantic soundness and historical precision; 4. unplausible harmonizing, and unscientific guesswork about textual corruption where inconsistencies seem to appear; 5. a theology preoccupied with peripheral details and thus distracted from Christ, who is the Bible’s focal centre. Such fears are understandable since professed inerrantists have lapsed in all these ways, especially in North America, and inerrantist scholars today have to disclaim all these pitfalls.
As there is a rationalistic inerrantism that bases belief of the Bible on proving it true, so there is a relativistic non-inerrantism that, by the light of logic, secular learning and critical know-how, claims to find in Scripture errors that do not really matter. Both are theologically objectionable, though both present themselves as sound and orthodox; but each errs by making human reason the arbiter of divine realities. However successfully faith in Scripture is shown to be reasonable and unbelief of it unreasonable, the warrant for actually and habitually believing it remains, objectively, the teaching of Christ and his apostles about its nature and place and, subjectively, the conviction of its divine authority that the Holy Spirit induces. On this twofold basis all Christians should commit themselves comprehensively in advance to trust and submit to all biblical teaching about Christ, salvation, life, world history, and every other topic that the text deals with, and labour constantly to fulfil that commitment as through Spirit-prospered study their grasp of Scripture grows. It matters less what words they use to articulate the authority of the Bible than that they live under it in this way.
This article by Vanhoozer is another helpful explanation concerning the question of the inerrancy of scripture: http://www.theologynetwork.org/biblical-studies/getting-stuck-in/the-inerrancy-of-scripture.htm