Most weapons and artillery are split by bore diameter, e.g. naval rifles of 203mm, 406mm etc.

Railguns and coilguns probably won't be classified the same way, I think. Cause if multiple models use a 25mm slug or what have you, but they perform differently, what's a good way to separate them?

Muzzle velocity? Like a 2km/s railgun versus a 5km/s one? Or input energy? That then puts forth what's a "realistic" number to power a railgun? Output energy/impact energy have the same problem.

As with artillery there should be some sub-types, say howitzer 88mm is quite different from a 88mm anti-air gun.

Same logic can be applied to railguns, but with the main metric being for example impact energy.

Let's say a navy 2MJ railgun with a range of 100 km, or a 50kJ man-portable one with penetration ability of 2000 mm plate steel at 5 km, etc.

Gauss

The gauss, abbreviated as G or Gs, is the cgs unit of measurement of magnetic flux density (or "magnetic induction") (B). It is named after German mathematician and physicist Carl Friedrich Gauss.1[2] One gauss is defined as one maxwell per square centimeter. The cgs system has been superseded by the International System of Units (SI), which uses the tesla (symbol T) as the unit of magnetic flux density.[3] One gauss equals 1×10−4 tesla (100 μT), so 1 tesla = 10,000 gauss.

I would say the best way to rate a railgun is by its Gs output.

Ammunition diameter x ammunition length x launch velocity, also including muzzle energy for those who don't want to work it out for themselves. They'll almost all be Armour Piercing Fin Stabilised Discarding Sabot (APFSDS) so that need not be mentioned unless different in some way, e.g.:

5x50mm 5km/s 98kJ Steel

This could be a man-portable crew-served tripod weapon or vehicle mounted railgun firing steel flechettes

Or, a more terrifying ship-launched:

50x1000mm 7km/s 919MJ DU Guided

Which would be a depleted uranium flechette with a guidance package used for bunker busting.

Or a tank-launched:

20x400mm 4km/s 19.2MJ DU

That pretty much gives all the information that anyone with any knowledge of ballistics would need to work out the terminal effects of the round and its flight performance.

Joules.

... but for railguns, it's the 'cartage' that will have the rating, and the rifle will have to be approved to fire it: "Chambered for the popular XM107 round!"

.308 verses .50 BMG

But those are just numbers that would make us wonder if it will penetrate 3/4 inch thick steel plate at 200 yards (which is no and yes, respectively). However that's the only single number to look at for "ballistic performance".

I think that if or when they come to market, railguns will be (hopefully) named akin to their caliber, but they will be rated in the largest weight 'cartage' that they can chamber and reliably fire. In all actuality, it's going to be called by whatever name given by whatever manufacturer produces the most prolific round (and eventually appear as a truncated, standardized version as deemed by the government). Often, new weapons are specifically made to use a premier cartage; not the other way around - they're at the very least, made alongside (I'm so tired of video games that a new rifle drastically changes everything, all the while firing the same cartage...).

They will not be rated in muzzle velocity because as you can see, the differences between those two cartridges is negligible, but their impact is not, due to a .50 BMG being about four times the weight of a .308, and traveling at basically the same speed.

The problem with portable railguns is their imaginary power supplies. Who knows, they might be called iRifles. Whatever they're called, the bottom line I'm looking for on a projectile is energy on target.

Perhaps the nomenclature will be as thus: "Certified to fire [XXX] grain, [.XX] caliber projectiles, at the UN specified minimum speed of 3k ft/s." ... because you're relying on the rifle to accelerate the projectile, the manufacturer of the rifle will have to be acclaimed by the projectile manufacturer (whom would get to name the cartage). Call the rifle whatever you want; it has to be rated to fire (in specific calibers, obviously) a given weighted projectile (at the more or less acceptable speed of 3k ft/s).

TL;DR: some combination of weight and caliber. One tells me if it fits in my gun, the other tells me how much of a mess it's going to make.

Current researchers classify railguns by their muzzle energy, such as the US Navy's 32MJ railgun, and researchers were looking to double the energy to 64MJ.

This really is independent of the size and mass of the projectile, you could have a 64MJ railgun firing a very small pellet at hypersonic velocity, or large cannonball shaped projectiles at a much lower velocity. However, we accept that current chemical tube artillery can have very different trajectories and terminal effects even if the same calibre; for example a 105mm howitzer has a much different profile than a 105mm L7 tank cannon (or a 106mm recoiless rifle, which was actually 105mm in calibre, but marked "106" to prevent confusion in the logistics train)

105mm Howitzer

105mm L7 on a German tank

106mm recoiless rifle

So railguns and electromagnetic cannon in general could be characterized by their muzzle energy, without too much distinction between the actual role of the weapon. This could be a secondary descriptor i.e. 64MJ naval surface bombardment railgun or 10MJ naval antimissile railgun.