However, to be strictly accurate, we need to recognise that there is a subtle difference between the two terms, as I will now explain.
The Bible is Infallible
When we say that the Bible is infallible we mean that it is the never failing, final authority, in all matters of faith and conduct. That is, despite the way society changes in its attitudes, we stand by the Bible's teachings when it comes to what we should believe, and how we should live.
Two examples will suffice to explain what I mean: many people today say that this country is a multi-cultural, multi-faith society and it is grossly intolerant to state dogmatically that there is only 1 way to Heaven. However, the Bible clearly teaches that there IS only 1 way to be saved, and that is through faith in Jesus Christ, the Son of God, as our Lord and Saviour.
Moreover, when it comes to conduct, society has undergone huge changes in the last 50-60 years, particularly in the realms of marriage and sexuality. However, the Bible is clear when it teaches that marriage is 1 man to 1 woman, and sex should be within marriage. Therefore, we stand by the Bible, not the ever changing rules of what is, and what is not, acceptable.
In the light of the foregoing, it is not erroneous to state that the Bible is infallible, BUT it does not go far enough.
The Bible is Inerrant
By the inerrancy of the Bible we mean that it is without error, not only in terms of belief and conduct, but also in terms of what is stated as fact. In other words no provable scientific fact, no provable historical fact, no provable geological fact, no provable archaeological fact and no provable geographical fact, will ever contradict what the Bible says.
I'm not stating that all we ever need to know in these fields comes from the Bible but, rather, that no provable fact, or discovery, in these fields, will be at odds with the Biblical record.
Over the years historians have questioned the veracity of the Bible with regards to places and people (for example cities, kings and rulers). However, discoveries made by archaeologists have substantiated what the Bible says. One example being the ancient city of Nineveh as mentioned in the book of Jonah. "Such a place never existed", said historians - until its ruins were discovered!
What do we say then, in conclusion?
Firstly, we can have absolute confidence in the Bible as the Infallible and Inerrant Word of God and use the two terms together as it is both.
Secondly, given that it is God's perfect Word, we should commit ourselves to reading, studying, digesting and living it, on a daily basis; it is the very life-breath of the believer and, indeed, our spiritual oxygen for living out the Christian life.
Thirdly, we should, unashamedly hold it up for all to see and urge upon others the necessity of believing its central message viz. "Christ Jesus came into the world to save sinners" - "repent, therefore, and be converted" 1st Timothy 1 v 15, Acts 3 v 19