Sorry, Steve
No pic. A Hornet looks like a miniature .30-30, with a rim and a long gently tapering neck. Most now use .224 bullets, same as .223 but usually in the 40 to 45 grain range. Small rifle primer. Popular powders are Alliant 2400 and IMR 4227, charges around 9 to 12 grains, velocitiy 1900 to 2200 fps roughly.
K-Hornet is a wildcat based on the Hornet with the shoulder blown forward by fire-forming to make a sharp-shouldered higher-capacity case. Same bullets, primers, powders.
It IS between 22 Mag and .223. More accurate than .22 Mag. A very good varmint/chuck round, overpowered for squirrel unless you load down. The first smallbore centerfire varmint-type round, wildly popular in its day between the wars and enjoying a resurgence today.
Flatter shooting, more power, and longer range than the .22 Mag, but quieter than the .223/22-250/.219 Donaldson class. It's agaain finding a niche as hunting areas get more crowded and nearer to dwellings.
A neat, interesting round with high accuracy potential in the right rifle. Unfortunately for its reputation it has been chambered in many not-so-accurate rifles. If I bought a a new Hornet today, I'd get a nice Kimber or Anschutz or equivalent. My experience with Ruger 77/22 doesn't lead me to think it would wring the best out of the Hornet.
Economical, too. A pound of powder should be good for up to 700 rounds.