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.

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 The cgs system has been superseded by the International System of Units (SI), which uses the tesla (symbol T) as the unit of magnetic flux density.[3] One gauss equals 1×10−4 tesla (100 μT), so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.

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.

[ammunition diameter] by [exit velocity]

Essentially, you notate the diameter of the weapon's accommodation, and then notate how fast it can get a slug of that size going. That latter would probably be a range of velocities, given that different lengths of slug will take different energy inputs to accelerate.

Also consider if you want to be able to shoot to wound instead of shooting to kill. Chemical propulsion doesn't allow for that, but a railpistol might.

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.