The real answer is, they don’t mean anything.
Company names tend to be like any other. You have companies that were named after the founder (or founders). For example, S&W was named after it’s founders, Horace Smith and Daniel Wesson. Glock, Winchester, H&K, and Colt are also examples.
There are companies that were named very descriptively. The best explanation would probably be through exact examples. IMI is simply an abbreviation of Israeli Military Industries. FN Herstal (usually referred to as FN) is Fabrique Nationale d’Herstal (or National Factory of Herstal).
SIG Sauer is an interesting combination of both. It’s actually two separate companies. SIG is Schweizerrische Industriegesellschaft, or Swiss Industrial Company. Sauer is actually J. P. Sauer und Sohn GmbH, which (I’m assuming) was named for the company’s original founders, though given it was founded in 1751, I can’t verify that off hand.
Companies that were named because someone liked the way it sounded, but don’t actually mean anything. Microtech, Freedom Arms, and Taurus come to mind.
The weapon names are created by the company. So in a lot of cases you’re looking at the result of market research guys deciding what to name something. Again, these names can be descriptive, H&K’s USP is derived from Universelle Selbstladepistole. Or, universal self-loading pistol. Or they can be entirely designed to the consumer, like the Colt Python, or the S&W Sigma.
As with the company, it’s not unheard of for a pistol to be named after the designer. FN’s Browning Hi-Power for example.
It’s also not unheard of for firearms to be named after their year of implementation. The 1911 pattern pistol is a classic example. It’s not always safe to assume this is the case.
For a partial trifecta, you can look at the AK-47 AK is short for Avtomat Kalashnikova. Avtomat is just Russian for Automatic. Kalashnikova is a female patronymic based on the designer’s name (Mikhail Kalashnikov). And, the gun was intended to enter service in 1947, though, that didn’t quite happen, it does reflect the general time the weapon entered service.
That said, the numbers don’t automatically mean anything. They can refer to general product iterations, Glock and SIG both do this. They can be picked to sound cool, Colt’s been guilty of this a few times. Or, they can actually have a fairly complex internal meaning, like many of the S&W automatics.
Numbers and letters can be combined to identify iterations in a firearm’s design. This happens by amending an “a” to the number. Further minor iterations can be indicated by adding a number after the letter. More substantial iterations can be indicated by increment the letter, and resetting the number progression. So an “a” then an “a1″, an “a2″, then on a major iteration, a “b”, followed by a “b1.″
Functionally, this works fairly similarly to software patch numbers, though those are delineated with decimal points.
Also, sometimes a letter will be appended to a firearm to indicate that it’s a specific variant. The H&K MP5K isn’t the 10th iteration of an MP5, it’s the “kurz” or “short” version. Though, the MP5 does have a series of A# variants, that are iterative. For the MP5K, the A gets applied after the K, so an MP5KA1.
Ammunition is almost as random, and it gets wedged comfortably in a weird state between Imperial and Metric measurements, sometimes with the same round existing in both.
Caliber is a decimal of an inch. So, .50 would be half an inch, .45 is 9/20ths, and so on.
A millimeter value is just the diameter of the bullet, so, that’s what 9mm means. Technically, you also often have to identify the length of the bullet under the metric system, to differentiate between something like 9x19mm Parabellum (the NATO version of 9mm you’re probably familiar with) and 9x18mm Makarov (the Warsaw Pact version.)
There are metric equivalent values for Calibers, it’s the same bullet, just under a different name. So, a 12.7mm round is going to be a .50. A .40 is a 10mm round, though it’s actually a 10x22mm, in comparison the “normal” 10mm round, which is 10x25mm. Which is why they use different names, even though they came out of the same R&D project. The .40 is a lower power version, developed after the 10x25mm proved too difficult to use.
Shotgun gauges are calculated through an incredibly archaic system. It’s the barrel diameter to fit a single lead ball of that fraction of a pound (dating back to non-scattershot, unrifled barrels). So a 12 gauge is chambered to take a musket ball that weighs 1/12th of a pound. A 20 gauge, 1/20th, and so on. 12 gauge works out to be roughly 18.5mm, if I remember correctly, but that’s a statistic basically no one uses.
If you’re wanting a useful takeaway from that, I’d say, settle on a round for the role you want, and don’t worry too much about making the ammunition match to real world cartridges, because the ones in the real world are an incredibly diverse arrangement.
I’m hesitant to even start a discussion about firearms types, in this context, because of how much history gets dragged in. The rise of automatic weapons in the 20th century is intertwined with the world’s wars. The submachine gun was something that, specifically, had a very hard time wining over entrenched military bureaucracies before the Germans started making heavy use of it in WWII. In turn that lead to the evolution of assault rifles in the final days of, and after WWII. Well, battle rifles, modern assault rifles were a further result of trying to take the 7.62mm automatic rifles and bringing them down into something more manageable, based on the ranges that combat was actually occurring at, rather than what military thinking thought they should be fought at.
When you start building your own setting, you have to decide how much of that is getting jettisoned, and how much needs to be brought over.