Instead of 9mm

What we call ".38 caliber" or "9mm" IRL is anything but. .38 Special is .357", for instance, as is the (aptly-named) .357 Magnum. Only one pistol cartridge actually fired a .38" bullet, 9.65mm ACP - and you've never heard of it, because it never entered production. (And for another outlier, there's .38-40, which fired a 10mm bullet. There's some speculation that the name is dyslexic, and it should've been called the .40-38 instead.)

This discrepancy goes back to the ur-9mm handgun: Colt's Texas Paterson. It (and the Colt Navy Revolver that came a decade later) established .36" as a revolver caliber, and later in the era, some .36-style cartridges loaded with heeled bullets, which actually were .38" give or take a few thousandths of an inch. After heeled bullets fell from fashion, the standard shifted to the largest bullet that could fit inside the case mouth, whence .357.

What happens in Andalusada, where Col. Colt is never born? Ballistics favors convergence - and for the sake of laziness, I'm ruling that this converges - but for that frisson of difference, the big successful caplock caliber was about a hundredth of an inch off.

And that, as I complained in a long-ago sonnet, changes everything.

8.8mm as a world-standard pistol caliber

IRL, late-19th-century military sidearms went in one of two directions. One of those directions was towards big-bore revolvers (the United States and Great Britain most notably), favored by forces that actually used their sidearms seriously. The other, favored by European continental armies that didn't often need to fire their sidearms in anger, was toward smaller bores, often the same diameter as the rifles they used (most famously in the Nagant revolver.)

In Andalusada, the second route is by far the less common one, for a fairly simple reason: the first trendsetting caliber of the smokeless era was France's 6.6mm, which was far too small for an adequate pistol. (Not coincidentally, France retained its 10.44mm revolver, which remains in service to the present day.)

• The first person to become really identified with 8.8mm is Eugen of Egypt, who bought one of the first caplock revolvers and used it astonishingly well for the minimal practice he did. (His Egyptian Diaries brought it to Saxon attentions for the first time.)

In this environment, 8.8mm took off, because of an important adopter: Patagonia - and because of power politics, the CRC en bloc. ACP cranked out tens of thousands of revolvers, which were copied by both the G.P. and Gran Peru and were exported worldwide. (Several of the standard 8.8mm cartridges, for both revolvers and semiautomatic pistols, originate in Cabralia.)

8.8mm as a rifle caliber

Nominal .38"/.357/9mm is also a rifle caliber, and it's all over the place again:

• Some of the oldest date from the the blackpowder era, measuring .376" (9.5mm) or thereabouts. The standard-setter in this class was .38-55 Winchester, which spawned lots of copycats (such as .38-72, also by Winchester) and a modernized version that lingers to the present day.
• .35 WSL and .351 Winchester cartridges were nominally .351", and hover around 8.91mm. (Why the duplication? Because the latter was meant to replace the former.)
• The modern standard is the .358/9mm, which dates back to 1906 in America and the 1890s in Europe. 9mm Mauser was standardized at 9.06mm; post-WW2, the global standard seems to 

Only one gun ever used 8.8mm bullets: the Winchester 71, which loaded .348 Winchester. Both gun and caliber were introduced in the middle of the Depression; both fizzled out in the 1950s. In Andalusada, where 8.8mm bullets are a much bigger thing, things are understandably rather different.

Unlike 8.8mm handguns, 8.8mm rifles are purely a child of the smokeless era. Once ACP began selling pistols on the global market, the world was starting to standardize on it already; the only new hardware involved was bullet molds for the rifles.

• 8.8x53mm ACP: If ACP themselves got on board with this, the obvious wildcat would be necking up (or possibly redesigning) 7.65mm brass for 8.8mm bullets. (I am not a wildcatter; I have no idea how well this would actually work.)

I am not a ballistician, but I can see some tentative uses for such a caliber:

• One niche it fills is that of the 9x57mm Mauser. Loaded to the same basic weight and fired at the same velocity, it'd have a slightly better ballistic coefficient; a decent deer cartridge, but a bit light for use in the Sudan.
• The first obvious niche I could see for it is as a woods gun, à la .35 Remington. On the northeast Atlantic coast (where feral pigs are a problem), .405 Ryalkirk is considered the sensible minimum, so it probably wouldn't have much of a New British following. On the other hand, the southern UCNA might use it more, and if it copied .35 Remington ballistics it'd be enough gun for hunting in the Mexican jungles.

The one place that 8.8mm hasn't taken off as a sporting cartridge is inside the French Empire, for a fairly simple reason: the tierseur was already established. The French tiers-pouce (~9.02mm) is roughly equivalent, and actually more widespread during the early smokeless era (tierseurs were among the first smokeless guns, albeit at a time when cost was no object); by the time 8.8mm rifles could plausibly sell on the market, the Modeste (and ammunition for it) was already available. More importantly, France is quite protectionist for its tierseurs, and anything an 8.8mm can do, a tiers-pouce of most any make can do better.

Outside of France, though (and a few places where the tierseur has developed a cult following), 8.8mm has the run of the industry.