First of all, the idea that the Scriptures are “inspired” are a post-Biblical thought (after the Hebrew Scriptures were composed) and mean different things to different groups.
First off, the Jews don’t believe in “inspiration” along the lines that Christians do. And while they currently refer to their collections of writings as “canon,” the truth is that Jews don’t have such a thing in the Christian sense of the word. For Christians, “inspiration” is a requisite to canonicity whereas among Jews it is their religion that has been inspired of G-d. As a product of inspired religion, the Scriptures have been accepted among the Jews.
“Inspiration” among groups like Jehovah’s Witnesses and Fundamentalist Christians clashes with what the word means among mainstream Christianity. For groups like Orthodox Christians, Protestants, and Roman Catholics “inspiration” refers to the entire process that went into creating the Scripture texts, including redactions and editorial changes. The “inspiration” process ended when the books were chosen for official canonization, not when they were first composed. Thus the several different endings to Mark’s gospel are considered canonical as are additions to John’s gospel such as the beginning to chapter 8.
But for Jehovah’s Witnesses and groups like them, “inspiration” is more like a dictation process usually between G-d and one writer at a time. The author of the written work is often described as little more than a conduit. “Inspiration” is also limited to the earliest or original writings only, none of which exist.
While it is true that the writers obviously didn’t see their works as “inspired” in the JW sense, this is not true about some of the Jewish texts as well as the redactors and their work that later went into the finalization of the Tanakh. The Mosaic Law was definitely considered to have divine origins by its composer(s), and the redaction/editorial process that came as late to these writings as the time of Ezra demonstrates that the redactors definitely believed they were handling a holy work from G-d. But this cannot be surmised from an immediate reading of New Testament texts.
Modern Bible translations are the result of ecumenical bodies which can include people who fully embrace one or several of the ideas of inspiration listed above and those who do not. A group of varied approaches allows for a more honest and critically produced text. The NRSV was created using a group of Protestant, Orthodox, Catholic and Jewish scholars as was the CEB. Currently the Holy See recommends that all official Catholic versions be composed by ecumenical translation committees only in order that Catholic translations can be placed at the service of all Christians. And the recent NJPS translation of the Tanakh has been embraced as the standard for rendering the Hebrew Scriptures into by practically all Christian scholars, as well as laypersons.
The reasons for the differences is due to the fact that English is a difficult target language. Unlike other languages which easily lend themselves to capturing Hebrew and Greek nuances, English makes literal demands that cannot be yielded from these tongues. Another reason for differences in renderings occurs because of attempts at creating “word-for-word” translations, a method which never exists in real language translating. But this type of formal equivalence is still considered popular in English, crippling the ability of Bible versions to accurately convey linguistic logic which defies English idiom in its most rudimentary elements. This causes stark differences in word choices, especially when made from Hebrew which due to being extremely terse has layers of meanings which are almost impossible to capture with simple English.