A translation is a translation, i.e., taking the words and meaning of one language and putting them into another language using its own words and meaning. Examples of this include St. Mark's rendering of Christ's cry upon the Cross:
And at the ninth hour, Jesus cried out with a loud voice, "Eloi Eloi lama sabachthani?" which means, "My God, my God, why hast thou forsaken me?"
A "rewriting" doesn't necessarily involve
translation -- things can be paraphrased or otherwise rendered in one language without directly
translating from another. This is particularly helpful to note when we are dealing with translation from Semitic languages like Hebrew and Aramaic into Indo-European languages like Greek, Latin, etc. This is because the Semitic languages form their words differently than Indo-European languages do. In Semitic languages, words are formed around consonantal 'roots' which are fit into templates which, depending on how the space around the consonantal root is 'filled in' with different vowels, tell us something of their relationship to the root which denotes the concept.
The example you'll find in every Arabic 101 textbook is K-T-B, which denotes something about writing (the general concept). From that K-T-B root, we get words like
ki
ta
b 'book',
ku
tu
b 'books' (plural),
ka
ti
b 'writer', ma
kta
ba 'library', ma
kta
b 'office', and so on.
Since the scripts of almost all Semitic languages* only obligatorily denote consonants and
sometimes long vowels, without some kind of diacritical marking there can be ambiguity as to what words that otherwise look the same actually mean. This is why you find those diacritics in Arabic (and Hebrew, etc.) only in texts where proper understanding and pronunciation is paramount -- like religious texts -- or in learner's texts (dictionaries, etc.) or in contexts where they are needed to resolve ambiguity (where the context alone does not preference one understanding over another, so you have to literally point out "no, it's this, not that").
Imagine trying to read a script that just says MRMNSM S FLS Is it "Mormonism is false"? Is it "Mermanism so fills"? Is it "Mirmanism's fleas"? Disregarding the fact that the latter two are gibberish in English (or I dunno...maybe someone's so fulfilled in their worship of male mermaids that they need to tell us about it, or maybe they started a cult that worships comedian and voice actor Eugene Mirman, and all they have to show for it is flea bites, and they're trying to warn us...), you can't really know as it is without contextual clues that you may or may not have.
Hence in early Christianity there was a bit of controversy concerning the Greek translation of the OT done in Alexandria, Egypt in the centuries before Christ, known as the Septuagint or the by the Latin numeral abbreviation LXX (for "70", referring to the number of translators who worked on it). You may remember it from the writings of St. Justin Martyr in the 2nd century, when he accused the Jews of embracing another text rather than this one, which he claims they previously used. The reason they could have even 'switched' to a different text is because of this ambiguity in the way the text was written -- if you fill in the consonantal text with different vowels according to your own reading, you get a different meaning. That's why Christians have traditionally used the LXX translation for their OT: not only do we believe that it probably represents an older tradition that was more or less abandoned by the Jews after the coming of Jesus Christ and the identification of Him as the promised Messiah (a claim which most Jews of His day rejected, mind you), but its readings support Christian -- specifically
not Jewish -- understandings of prophecies that we believe to be told of Christ in the OT. For instance, there is a portion of the Psalms (I can't remember which one exactly, as the Psalms are numbered differently in Eastern and Western Christianity) that the LXX translated as "They pierce my hands and feet" (obviously in reference to Christ's crucifixion), but which is translated in the later Masoretic text (which was used as the standard OT source text in Protestant Bibles and some Catholic Bibles) as "There are lions at my hands and feet".
Which of these is a translation and which is a 'rewriting'? Obviously if you have an ambiguous source text
based on features of the script used to write it, it can mean several things without any side being a 'rewriting' -- hence St. Justin's objection to the Jews of his time is that they had switched
from one translation to another, and hence 'corrupted' the scriptures by their new, specifically Christ-excluding understanding...all without even one letter changing from the source text. (NB: There was once a belief that the Jews held a council called the
Council of Jamnia specifically to address Christian claims by inserting the appropriate diacritical marks to standardize the reading of the text away from Christian readings, but I don't think most scholars actually believe that this was literal historical event anymore. I'm not 100% sure about that, but I think the balance in academia points to it being doubtful or fabricated. I do still hear it repeated in some churches sometimes -- even my own -- as it was a very popular belief that went unchallenged for about a century, and hence can be found in many fairly modern academically-minded books where it is taught as a literal historical event. As you can read at the link, it only began to be widely rejected in the 1960s.)
(*Long aside: the Ethiopian languages written in the Ge'ez script buck this trend by obligatorily marking vowels by means of various 'descenders' which are fused to the consonant itself, making every character a syllable, e.g., here's your name Mormon, for instance: ሞርሞን Mo-rɨ-mo-nɨ . In this transliteration, the ɨ vowel, which some prefer to transliterate as ə or ä -- I don't know that there is a standard -- represents a kind of central vowel which may be elided/not spoken, so as to produce "Mormon", rather than "Morimoni"; this is how the script can represent written consonant clusters like አምሐራ A
mhara or ኦርቶዶክስ Ortodo
ks, which are written but not spoken like 'amɨhara and 'Orɨtodokɨsɨ. This is distinctly Christian development: before the acceptance of Christianity, the script hadn't had these fused vowel markers, and hence remained consonantal and non-syllabic, as Arabic, Hebrew, Syriac, etc. are.)
Because he wasn't doing the same thing. He was working with something that was
already a translation into English, and perfectly understandable as it was, and he added other things in his 'translation' that were not based on anything in the source text, but on his own twisted belief.
It would be like (if I believed this;
I do not -- this is an example only) if I inserted into the Biblical text, a propos of nothing, something that said "And then Jesus said 'Everyone needs to be Orthodox, because only Orthodox Christians get saved.'" That may very well reflect my own ecclesiological/soteriological belief, but if it is not in the source text I am working with, then I'm really just putting my beliefs in Jesus' mouth, aren't I?
Similar charges
are in fact made by some Catholics and Eastern Orthodox Christians against Luther, for supposedly adding the word "alone" into the Epistle of St. Paul to the Romans, so that 3:28 would read in the German translation: "So now we hold, that man is justified without the help of the works of the law,
alone through faith"
The word "alone" apparently does not appear in any of the manuscripts of that text. so the charge is that was only added to support Luther's 'Sola Fide' doctrine. (I, not being RC or EO, don't know anything about this beyond that the controversy exists, and don't really care to weigh in on it, out of respect for our Protestant friends on this forum who are so often invaluable in the continuing conversation against non-Christian faiths.)
It depends on who you ask. And probably if you ask all of those same people what they think about Joseph Smith's additions to the Bible in his 'translation' work, they will all say it is completely unacceptable and rejected.
That ought to give you pause.