Sure, there's carving your skis and then if you can't, there's steering the skis around the turn, but is that all there is? As we think about this and break it down in more detail, there's a lot more to it... let's see if we can get anywhere by simply cataloguing them all.
Let's catalog types of turns that we can do on skis and speed control options and overall control as well as the skill required for a good execution of each - this is all in terms of skiing a blue/black run. Greens and double-blacks are extremes:
stivoting - usually some pivoting to start it, but mainly forceful skidding
This is intended to give anyone enough criteria to choose one type of turning for whatever context/conditions/strenght/skill/speed... For racing there are more tactical considerations when choosing in any given turn, i.e. where is my balance at the end of the movement, how fast can I transfer balance etc.
Here's some tactical situations AS I SEE THEM, assuming I can do either, skill-wise:
Next you get outside and go skiing, try some of these. See for yourself how easy it is to change the turn shape, how easy it is to control the skis, how much speed can you dump while in relative control...