My experience tells me that the major differences in the "two" types of skis are longitudinal and torsional flex, tail shape, and camber.
Generalized ski type #1
Stiffer skis for groomer skiing (stiff across and along the length of the ski) bear up well when they are bent under high pressure. They don't twist along their length nor bend and unbend like a wobbling diving board when the snow is not smooth. These skis instill confidence in charging speedsters who know how to get them on edge and engage them in the snow, something that many skiers don't know how to do. If such a ski has a flat tail with sharp pointed corners, that's useful for holding onto the carve untill the very end of a turn which is also good if the skier knows what to do with the end of the turn. Such a skier needs to know how to let go of that turn decisively. This is something people who know how to carve on hard snow can do but it's not not something most recreational skiers are familiar with. Strong camber presses the tip and tail into the snow so the whole edged ski engages, an essential quality in skis making carved turns.
Put an intermediate skier on such a ski, on hard snow, and those tips and tails are going to catch and throw those skiers around.
Short-cut terms are called for in marketing. Should this type of groomer (front-side) ski be called an "Expert" ski? Or a "Power" ski? Or something else? What word would guide the right skier towards this ski while repelling the wrong skier - without judgement and without gender implications?
Do most recreational skiers want to think and read and talk about tail shape, longitudinal and torsional stiffness, and camber when they choose a ski? Or do they want a short-cut description that matches what they think about themselves as skiers? Marketers think people prefer simple descriptions, so that's what they give them. Those other factors are rarely described in ads for skis.
Generalized ski type #2:
Soft skis easily bend, like a diving board the long way, under low pressure. The pressure the ski feels will be low when the ski is kept flattish, when the skier is traveling slowly, and/or when the ski is edged but the skier has not engaged it in a carve. That bend helps the ski create round turns for the skier, so it's a good quality for that skier. A stiffer ski will not bend, forcing the skier to rotate the ski manually through the turn, which is not so good. Rounded off tails on this type of ski, that are turned up, let go of the turn when it's over, rather than sending the skier off towards the side of the trail in a runaway traverse. Such a tail is important if a skier is a bit aft in their stance. (That tail is also useful if a skier capable of carving chooses to make most turns skidded in order to control speed on crowded slopes, so rounded tails will be found on all kinds of skis, a big sign that the qualities of the generalized two types of skis get blended a lot.) A ski that twists at tip and tail when they are under light pressure, (it's not torsionally stiff), and that has softer or less camber, will allow its tip and tail to smear across the snow in a skidded turn. That's good for these skiers because the alternative gets ugly. Such skis can take off on their own, throwing the skier down on the snow, if the skier's precision is off. Terms you might hear describing this quality are "forgiving" and "large sweet spot." Basically, if a skier is imperfect at staying centered, the ski tail doesn't catch and send them for a joy ride.
These comments are about groomer skiing. I'm a New England skier well-versed in hard snow technique. I am not familiar with how the division of all skis into two types, or a blend of two types on a spectrum, works for fat off-piste skis meant to be used in fresh ungroomed snow.