..classify the calibers? High, Intermediate, Low, etc.? Where do you draw the lines?
High power is a nebulous term, because it can only mean something when compared to something else. A .22LR is high power compared to a BB gun.
The media generally thinks its anything centerfire, these days. Or, at least that's the way they talk.
I use the general classification system that came about during the Second World War, and refined a bit afterwards. (this is focused on military cartridges, but can be applied to sporting ammo as well, in general)
Prior to WWII, there were pistol and rifle rounds as general groups. During WWII, the "intermediate" cartridge was developed, for the
Sturmgewehr.
Pistol class rounds were those in common use at the time, 9mm, .45ACP .38 Special, etc. (.357 was included) Rifle class rounds were the standard infantry rifle rounds, .30-06, .303Brit, 7.62x54R, 8mm Mauser, etc. Intermediate class rounds were anything that was more powerful than the traditional pistol class and less powerful than the rifle class.
When speaking only of civilian sporting rounds, there is a lot of ..flexibility, because of advertising claims, and general use of terms, which differ in different eras.
As one said, at one time 'high power" and "high velocity" were used virtually interchangeably. And, at one time, anything that beat black powder speeds was "high velocity".
"Express" was, at one time, a term denoting high power, conjuring up the awesome power of a speeding express train.
"Magnum", referred to the case size (bigger than standard), originally a wine industry term. Since bigger cases meant more powder, and therefore, more power, "magnum" quickly came to mean more power, as well.
All the hunting regulations about energy requirements could be used as a basis for classifying rounds, BUT, they are hunting regulations. Game Laws. Their definitions and restrictions are not based simply on what levels of power are needed for a clean kill at a given range, but also on many other factors. Including what they believe is best for the sport, and also what the overall population of hunters can use effectively, for the game hunted.
High Power in a match means whatever the match operators say it means. High Power in the media means whatever they want it to.
Don't get you information about guns, the law, medicine, love,sex, personal relationships, basic laws of physical reality, or a host of other things, off a screen alone, and you have a better chance of not being misled.