They both are similar in definition as it has been pointed out already. Evangelicals started using the term inerrancy about 30 or so ago, because of those who were rejecting the infallibity of Scripture by stating that the Bible was only infallible in areas of doctrine. When we state that we believe that the Bible is infallible we are stating that is without error.
Actually, a bit longer ago than that. Evangelical colleges and seminaries used inerrancy rather widely from sometime after the Fundamentalist-Modernist dust-up until the 1970s when institutions such as Fuller changed their doctrinal statement away from inerrancy.
The Battle for the Bible, penned by former Fuller prof and
Christianity Today editor, Harold Lindsell (1976) and his sequel,
The Bible in the Balance (1979) followed the defections from inerrancy in a variety of denominations, including the Lutheran Church and SBC, and institutions such as Fuller (Chapter 6 - "The Strange Case of Fuller Seminary").
Dr. Dan Fuller gave an address at the Evangelical Theological Society in December of 1967, later printed as: "Benjamin B. Warfield’s View Of Faith And History * A Critique in the Light of the New Testament."
Journal of the Evangelical Theological Society Volume 11 (11:75). His proposed "corrective" to Warfield presaged the change in Fuller Seminary's doctrinal statement that followed just a few years later. It has variously been dubbed infallibility, limited inspiration, partial inerrancy, etc. He wants to claim that the Bible is "infallible" in that it unerringly leads us to salvation. However, it is free to have historical, scientific, and factual mistakes in it.
Since then, we have witnessed numerous evangelical schools backing away from the word "inerrancy" due to the perceived cultural baggage attached to it, because of the implied conflicts with secular science, and as their professors have continued to achieve terminal degrees from secular schools inhospitable to inerrancy.
Maybe I'm just wired a little too much like brother Grymir and enjoy tweaking my liberal friends
too much. But, I proudly wear the term inerrancy and enjoy my sophisticated brethren clucking their tongues and shaking their heads.
BTW, Dr. Fuller's apartment is just a couple of hundred yards away from me at the time of this writing. Talk about cognitive dissonance for a guy like me. He is the most loving, humble, gentle man you could meet. But, on this topic we are miles and miles apart.
In another thread, I observed that, strictly speaking, "inerrant" would mean that you got a 100% on the algebra test; "infallible" would mean that you knew it all perfectly. I have often been inerrant, but never infallible! It is curious how the evangelical world has fixated on the less comprehensive term as the one claiming a stricter theological position and the more ambitious term for the looser view.