Im not an evangelical, and within evangelicalism there is a wider range of beliefs than we often give credit. So I don’t think I can really answer your question directly. Some others may be more equipped for that.
However, a resource you may be interested in reading that I found fascinating is this book of essays and responses from five Christians who all have different views on biblical inerrancy. They contend for their view in an essay and then respond to one another. I found it helpful to understand what other people believe about inspiration/inerrancy which helps me understand the way others view the text I dedicate my life to researching and studying. You might like it based on your question.
It isn't a direct study which I conclude this from. I'm drawing my argument from one that Michael Bird, who has written in Christian circles against inerrancy, made comparing the confessions of faith held by different global denominations:
>So the 60 million Anglicans in the global south hold to the Thirty-Nine Articles, with its reference to the “authority” and “sufficiency” of Scripture for salvation, leaving open how Scripture relates to history and science. The 75 million Presbyterians around the world, with major concentrations in Brazil and Korea, hold to the Westminster Confession of Faith, which affirms the “infallible truth and divine authority” of Scripture. The 2 million members of the Church of Southern India believe that “the Scriptures are the ultimate standard of faith and practice.” The Baptist World Alliance, representing some 41 million Baptists, in their Centenary Congress of 2005 declared that “the divinely inspired Old and New Testament Scriptures have supreme authority as the written Word of God and are fully trustworthy for faith and conduct.”
>If I'm not mistaken, both would affirm inerrancy, but would formulate it a bit differently, but that's what I heard, and I don't know the details of it.
That's accurate. They both affirm inerrancy. However, I'm sure that Vanhoozer would affirm what Mohler means when by inerrancy, and I'm not sure that Mohler would consider Vanhoozer definition to be a proper inerrant view. They interact in the book Five Views on Biblical Inerrancy, which I highly recommend. In the book Vanhoozer defines inerrancy as:
>the authors speak the truth in all things they affirm (when they make affirmations), and will eventually be seen to have spoken truly (when right readers read rightly).
Here is a video of Vanhoozer describing his position from a conference based on the book.