556 was the measure of the inner diameter of the rifling of a barrel of a gun that shot 556.
Metric is confusing. That's why for most shotguns, we measure the width by the number of lead spheres of that diameter that would equal one lb, eg a 12 gauge shotgun is the diameter of a 1/12lb sphere of lead.
Nobody knows how big 18.53 mm is, but everyone knows what a 12 gauge shell looks like.
Oh, and gun powder is measured in grains, maybe early smokeless pellets were about the same size as grains of wheat.
he's serious. The old casting method for round shot was to dump a measured amount of molten lead from a tower into a pool of water 40 feet below. the molten lead would form a sphere in free fall and fully set in the water, so it was convenient to define gauge diameter by fractional weight of a pound. Twelfth pound sphere fits a 12 gauge gun, etc.
The problem is it's impossible to tell whether you're joking or being serious. Throwing molten metal off the tower sounds like the most ridiculous thing ever, but apparently is a real thing.
Here's where it gets political. I learned about shot towers in passing years ago and thought that was a good idea. You learned about shot towers in passing, but then with a detailed explanation, still thought that was ridiculous. One of us is prone to rational thought and the other is not. This is a 17th century conversation happening now.
No problem. There's always a reason, and usually a pretty interesting one, for old odd hold overs like this, but it's been 200 years since shot towers were a thing, only history buffs and muzzleloader enthusiasts really know about these.
Grains as a measure of weight comes from the Troy weight system, think Troy ounce of gold. It is a very old system that for a long time was mostly used by apothecaries and probably has its origins in Ancient Rome.
Grains Apothecary is used to measure powder charge weight is because it was a "fine" enough scale for measuring small amounts of things that if you get it even a tiny bit wrong, can kill you. So, ammunition manufacturer's looked around and scales used for accurately measuring small amounts of drugs were commonly available, so they went with that.
Cool side point: Powder charges are checked by weight and dosed out, (or thrown), by volume as it has always been done since the first gonnes were a thing.
The case is both shorter and narrower than 556/223, so it won't even sit right in anything not designed for it. But FN makes quite a few guns that use it.
Even the "metric" measurements for firearms ain't necessarily true measurements either. Lots of them get rounded off or simply depend on just how they made the measurement to start with, (land to land or groove to groove). In any case a bullet diameter is almost always going to be just a tiny bit larger than actual bore size for modern cartridge bullets.