First, there's the many ways of spelling it. Karshuni, carshuni, carchouni, carschouni, karschuni, karšūnī, karshūnī, karschūnī, garshuni, garschuni, garšūnī, gerschuni, gershuni, geršūnī or even akaršūnī and akarschūnī - you name it, it's somewhere out there. Which is the correct one is anybody's guess. According to Julius Assfalg's brief yet exhaustive and even after 26 years unsurpassed overview of the subject (3:297-298), this is a much debated question among eastern Christians. Eminent scholars like G.S. Assemani and Alphonse Mingana believed it should be garshuni/garšūnī and considered the form karšūnī a Maronite corruption. On the other hand, many believe the correct form is gershuni, as it derives from Geršūn, the Syriac form of the name Gershon / Gershom, Moses' firstborn son, who is supposed to have invented this practice. The form with initial k- is firmly established in French and German traditions, while the English-speaking scholars seem to prefer garshuni and its derivations. To each his own, I would normally say, but in this digital age, a line has to be drawn somewhere. Searching for the same term with small variations over and over again just isn't fun. I'm taking this up with the European Commission, they should be able to settle the matter in no time at all.
Then there's the many meanings of the term - especially when it comes to manuscript catalogues. In the strictest sense, karšūnī is a term for manuscripts or printed works in Arabic language in Syriac script. Simple enough: language - Arabic; script - Syriac. Makes sense, right? Well, no, not really. It does not refer to a different variety of Arabic language the way the term Judeo-Arabic does - moreover, Arabic-speaking Christians used both Arabic script and Syriac script when writing Arabic. Nor does it describe a variety of the Syriac script adapted for writing Arabic (as is the case with the term bosančica, Cyrillic and Bosnian/Croatian) or a ductus used more or less exclusively for writing Arabic (as with nastaʿlīq and Persian/Urdu). The best way of defining karšūnī would be saying it's a practice of writing Arabic texts in Syriac script. This practice did not require any modification of the script (the way Cyrillic used for Turkic or Uralic languages did) nor did a separate ductus develop for writing Arabic. And thus in many manuscript volumes written in Syriac script, a text in Syriac is often followed by a karšūnī text written by the same hand in the exactly same serṭō. Add to that the formerly standard practice of Western libraries to catalogue manuscripts by script and not by language and it's 'Hello, Mr. Aspirin' every time you consult one of the older ones.
The Judas apocryphon mentioned recently at the Apocryphicity blog and the respective entry in the Cambridge Syriac collection catalogue is a classic example of the mess this can create. The physical description of the volume in question (Add. 2881) includes the following:
The writing is usually an unsightly cursive Karshuni, but some pages are written in a better Egyptian Arabic hand (e.g. ff. 175 b, 176 a, 245 a, 247 b —249 a, 258 b, 281 b, 282 a, 290 b, 291 a, 299 a— 301 a).
First off, "unsightly cursive" is definitely out of place here. "Unsightly cursive serṭō / jacobite " would be fine and so would "unsightly cursive madnḥāyā / nestorian". Even "unsightly cursive esṭrangelā" would be perfectly OK, though somewhat remarkable, since karšūnī texts were very rarely written in esṭrangelā. But "unsightly cursive Karshuni" just isn't right - "cursive" is an adjective used almost exclusively of writing and as I pointed out earlier, karšūnī is not a type of script. But never mind, I can live with that. The author of this particular entry apparently thought Karshuni was a designation of a type of Syriac script, which is why they also included the bit about "better Egyptian Arabic hand". We can thus assume that ff. 175b, 176a, 245a etc. are written in Arabic language in Arabic script while the rest is written in Arabic language in Syriac script, right? Well, no. According to the catalogue, folios 2b through 298b are written in Arabic language and Syriac script. This also includes ff. 175b, 176a, 245a, 247b —249a, 258b, 281b, 282a, 290b, 291a - all of which are supposed to be written in that "better Egyptian Arabic hand". Only ff. 299a — 301a are, as expected, written in the Arabic script, as are some notes on f. 307b. The rest seems to employ serṭō. At this point I'd like a glass of water with my medication, please. And I can consider myself lucky not dealing with texts in languages other than Syriac or Arabic written in Syriac script, such as Turkish, Armenian, Persian or even Malayalam (although to be fair, writing in Malayalam required some adapting and the script itself is legitimately referred to as "gerisoni"). Once we include those, karšūnī takes on a new meaning very similar to ajami.
And finally, there is the issue of the original meaning and the etymology of the term - though unlike the previous ones, this one is more theoretical than practical. We've already seen one attempt at an explanation (derived from Gershon / Gershom) and if you did not find it very convincing, I can't blame you. Other alternative etymologies proposed do not fare any better with regard to credibility:
- karḵūnē (a diminutive plural of ܟܰܪܟܐ [karḵā] = "rolled", also "codex") meaning "small round (i.e. letters)" - which, again, refers to a type of script or a ductus
- Syriac verb ܓܪܰܫ [graš] meaning "to draw away", hence "foreign, imported writing"
- Persian kār + Šūnī, i.e. "the work of Šūnī" (why Persian?)
- a diminutive form of Syriac ܟܰܪܣܐ [karsā] = "belly", i.e. "(letters) with small bellies" (again with the type of script)
- and finally, the trusted option of a derivation from a personal name.
As you can see, we're drawing a blank so far. It would help a lot if we knew where the practice was started and who first used the term, but we don't. All that can be said for certain is that the Wikipedia entry is quite wrong: there is no evidence that Eastern Christians wrote in Arabic before the end of the 8th century AD when (according to Graf) Maronites took the point and Nestorians and Copts followed suit. Nor is there evidence that Syriac script was used to write Arabic when "Arabic script was not yet fully developed and widely read". Such use of Syriac script cannot be ruled out, of course, but it simply doesn't matter: when Eastern Christians adopted Arabic language, they also adopted Arabic script. Up until the 13th century, karšūnī was reserved for titles, chapter names, notes and such, while most of what was written was written in Arabic script (such as the production of the Palestinian Melkites analyzed by Joshua Blau ). Karšūnī manuscripts grew in number in the 14th century and the next century marked the beginning of karšūnī's golden era which lasted well until the 19th century and survived even the introduction of printing machines. This is what we know for a fact. The rest, like the origin of the practice and the meaning and the origin of the term - not so much.
And so we are left with Assfalg's (3:298) observation to that effect and his brief remark that the earliest recorded usage of the term in European sources is the preface to Gabriel Sionita's and Faustus Naironius' edition of Novum Testamentum Syriace et Latine printed in Rome in 1703. Well, we were, until 1991. This was when Hartmut Bobzin published a brief yet fascinating article  antedating the term by at least 146 years. It was found in a manuscript by Johann Albrecht Widmanstetter who prepared the first European printed edition of the Syriac New Testament. The manuscript in question contains, among other things, a fragment of a Latin translation of Kitāb al-ādžurrūmīja, a famous compendium of Arabic grammar (original here). A translation of one of the first lines of Kitāb al-ādžurrūmīja ("Partes orationis sunt tres...") is followed by a brief excursus into comparative Semitology which includes these comments on the Aramaic language (pardon my very bad translation):
... Aliter syros scribere, babilonios aliter, et differentes ab utrisque hebreos qui e babilone in patriam redierunt. Deinde aliam esse scribendi rationem Jonathe, Onkelo, aliam Danielj et Jobis historie authori Mosj, aliam postremo Christianis quos Maronitas vocant, qui Chaldaico sermone in sacris utuntur, arabico vulgo passim, hunc ipsi vocant קרשוני illum chaldaicum quem Syrum adpellant.
... The Syrians use a different writing, so do the Babylonians, and the Hebrews who returned from Babylonia to their homeland use a writing different from both those. And thus one should mention first [targum of] Jonathan and [targum of] Onkelos, then the story of Daniel and Job written by Moses and finally the Christians who are called Maronites who use the Chaldaic language in their services and colloquial Arabic elsewhere, and this they themselves call קרשוני in that Chaldaic which they term Syriac.
As Bobzin points out, it is interesting to note that Widmanstetter speaks of language and not writing. It is also interesting to note that his version of karšūnī (I lost count, sorry) begins with a qoph and not a gimel, which may rehabilitate the form with initial k-. Or not, as it depends on where the form originated. Unfortunately, Widmanstetter's notes are not helpful in this regard and so the etymology and the origin of the term karšūnī are still lost in the mists of time. Ah well, maybe I'll find something. And while I search, remember: Arabic language, Syriac script. Like this:
 BLAU, Joshua: A Grammar Of Christian Arabic (Fasc. I-III). - Louvain : Secretariat du CorpusSCO, 1966-1968
 BOBZIN, Hartmut: Über eine bisher unbekannte Europäische Bezeichnung des Terminus 'Karšūnī' . - Journal of Semitic Studies, 1991, XXXVI/2, pp. 259-261
 FISCHER, Wolfdietrich (Hrsg.): Grundriss der Arabischen Philologie. Band 1: Sprachwissenschaft. - Wiesbaden : Harrassowitz, 1982, xiii., 362 p.