Is there a distinction between “victuals” and “vittles” that exists in writing but not in speech?

Spelling and pronunciation do not necessarily correspond to one another in English. This difference of spelling emerges in the early modern period.

Victuals (OED) has had a number of spellings in Middle English, usually with vit- or vyt-. These spellings were closer to the Anglo-Norman spelling vitaile. As Middle English spelling is largely phonetic, forms with vit- and vyt- were also pronounced with a /t/.

As English spelling began to standardize in the early modern period, sometimes spellings would change to reflect concerns beyond pronunciation, like perceived etymology. In this case, victual in spelling assimilated the spelling of an older Latin cognate (victus, food) while retaining the older pronunciation. These spellings are evident in lexicons as early as An Alveary or Triple Dictionary, in English, Latin, and French (John Baret, 1574):

• Pertayning to meate or victual: also base: simple.

Meanwhile, the vit- form persisted and eventually became vittle. It appears in some early lexicons, like Richard Mulcaster's The First Part of the Elementary (1582) (vitail), but most lexicons thereafter default to vict-, and victual is the standard spelling in Samuel Johnson's 1755 Dictionary. Vittle was preserved as a dialectal usage, which was useful for representing nonstandard speakers or informal usage in writing:

I must confess your wine and vittle / I was too hard upon a little (Jonathan Swift, "Stella at Wood Park," 1723.)

He was drunk, and weaving about in his saddle; he was over fifty year old, and had a very red face. Everybody yelled at him and laughed at him and sassed him, and he sassed back, and said he’d attend to them and lay them out in their regular turns, but he couldn’t wait now because he’d come to town to kill old Colonel Sherburn, and his motto was, “Meat first, and spoon vittles to top off on.” (Huckleberry Finn, Mark Twain, 1885)

Is there a distinction between “victuals” and “vittles” that exists in writing but not in speech? I think the short answer is yes. However, it's not a difference in the connotation of that single word, the way there's a distinction between, say, "terse" and "curt." These two spellings belong to completely different registers.

When writing we have the option of spelling it either victuals or vittles, making the second choice when we want playfully to evoke the supposed language of cowboys. As the excerpts in the Merriam-Webster entries seem to show, the writers who intend a light touch spell it phonetically, and the tonier writers spell it with the silent c.

Right. Except that there's another difference:

Victual can be a verb, synonymous with "provision." Victual, victuals, victualled, victualling. We see this verb form in three of your four example sentences. I claim that these writers had no choice, because...

Vittles is only ever a plural/mass noun, as far as I'm concerned. *Vittle, *vittles, *vittled, *vittling. ("What are you doing with that knife, Herr Wagner?")

You can victual your ship or your army, but you cannot "vittle" it. Load up the chuck wagon with vittles, yes. *Vittle the chuck wagon, no.

You can invite your epicurean acquaintance to victual with you (come on over! we'll tear a bird together!), but you cannot invite them to "vittle" with you. Chow down on some tender vittles, yes. *Vittle on chicken wings and beer, no.

Basically, "vittles" is a noun for cowboys; "victual" is a verb for military historians, a noun for Ren Faire attendees, and both for pretentious gastronauts.

N.B.: There is no non-loaded spelling of this word. If you want to refer to "vittles" without sounding like a cowboy, you don't write "victuals"; you write "food"!

By the way, How is "victualling" pronounced? — I didn't know this myself. I would have guessed "vittling" and "viktyueling" with about equal probability, tending toward the latter (and wrong) pronunciation.

This seems to be an American vs. British English issue.

For one thing, the Oxford English Dictionary doesn't have an entry for vittles, though it does for victuals.

For another, in the Corpus of Contemporary American English (COCA), there are 126 hits for victuals and 117 for vittles.

In contrast, in the British National Corpus (BNC), there are 25 hits for victuals and none for vittles.

As far as your question about whether there is any difference in meaning, you basically answered your own question: no, there is no difference in meaning, but there might one of register, namely, vittles is more informal and humorous.

Vittles not a deliberate misspelling of victuals

There is some suggestion in the comments and the other answers that vittles is a deliberate misspelling of victuals that matches the pronunciation of the latter more closely. However, the following note from Merriam-Webster would seem to dispute that (link; scroll down):

If you're hungry for the story behind victual, get ready to dig into a rich and fulfilling history. The word derives via Middle English and Anglo-French from the Latin noun victus, meaning "nourishment" or "way of living." Victus derives from the verb vivere, which means "to live" and which is the source of a whole smorgasbord of other English words like vital, vivid, and survive. It's also the root of viand, another English word referring to food. There's also vittles, a word that sounds like it might be an alteration of the plural victuals but which actually entered English a century before victual.