“Yet the KJV is quite close to the Douay–Rheims Bible, with some significant exceptions such as penance for repentance.”
It is hardly surprising that the current Douay–Rheims Bible is close to the KJV, since the original Douay–Rheims Bible was one almost no one wanted to ever use.
“The New Testament was reprinted in 1600, 1621 and 1633. The Old Testament volumes were reprinted in 1635 but neither thereafter for another hundred years...Much of the text of the 1582/1610 bible employed a densely latinate vocabulary, to the extent of being in places unreadable. Consequently this translation was replaced by a revision undertaken by bishop Richard Challoner; the New Testament in three editions 1749, 1750, and 1752; the Old Testament (minus the Vulgate apocrypha), in 1750. Although retaining the title Douay–Rheims Bible, the Challoner revision was a new version, tending to take as its base text the King James Bible...”
https://en.wikipedia.org/wiki/Douay%E2%80%93Rheims_Bible
Since 1750, the Douay–Rheims Bible has largely been the KJV with Catholic theology inserted so the ‘faithful’ would not be ‘deceived’ into ‘error’ by reading what the Word of God actually says.
Which is another thing that sees disagreement, with some RC purists insisting upon the original DRB.