The American Jesus has provided this great breakdown of total inerrancy vs limited inerrancy. I’ve usually heard “limited inerrancy” referred to as “infallibility” and so I’ll use the terms interchangeably here.
Let’s get the key point up front: the general definition of the doctrine of inerrancy is that the Bible is without any error of any kind. Not historical, not geographical, not grammatical, not scientific, not anything. Some Christians consider this a fundamental and if you don’t believe it then you aren’t a real Christian. Which excludes the vast majority of Christians today and throughout church history.
Limited inerrancy, on the other hand, claims that the Bible is without error in respect to its purpose: “God-breathed and useful for teaching, rebuking, correcting, and training in righteousness” (2 Tim 3:16). It doesn’t try to push behind what Scripture claims of itself, though. I personally like the term “infallibility” better just because “limited inerrancy” is more explicitly saying that the Bible is not perfect in the historical/geographical/scientific facts while infallibility just says that it really doesn’t matter if it is correct on those facts or not. On the other hand, I have heard a lot of confusion on how it differs from inerrancy, a difference which “limited inerrancy” makes clear.
To put this bluntly, those who insist that inerrancy is a fundamental of the Christian faith are heavily biased by the skewed priorities of the modern era. Fact is what matters to modernist thought. Cold, hard, propositional fact. It goes hand in hand with the legal framework for understanding Christianity, where the goal is to be in Heaven at the end of the age instead of in Hell, since all that matters is finding that key belief or those key beliefs that gets you on the right side of the verdict. Depending on who you ask, the beliefs – as pure “objective” propositions – will vary, including sometimes including biblical inerrancy. Regardless, the belief in inerrancy and especially the concept that it is a fundamental is clearly a symptom of this proposition-driven attitude.
But didn’t Jesus say that he is the Truth (John 14:6)? Sadly many modern Christians twist this heavily into talking as though facts about Jesus are the truth that lead to the Father. The key to this form of Christianity is intellectually accepting the right propositions (about Jesus to start with, but maybe some more after that). But that isn’t what Jesus said! Or what any other person in Scripture said! Or what any of the church fathers and mothers said! They all, consistently, seemed far more interested in a truth that is more incarnational than propositional. In particular, God’s incarnation as Jesus and how we should incarnate building our life around him. It really astounds me how much many Western Christians act and teach as if the Bible is there to be a systematic theology text as well as a science text and a history text when it pretty clearly has no interest in doing that itself (especially since such things didn’t even exist for 1500 years after the last of it was written).
This is why I tend to say that historical, scientific, geographic, and grammatical details are just really not that important. Most scholars would agree that a lot of those details in Scripture are true in the modernist propositional sense and some of them aren’t. But it doesn’t matter. It doesn’t change a thing about the kind of Truth that matters, the real Truth, the incarnational relational Truth, the still-living-and-with-us-today Truth, the Truth that sets us free.