Short radius turns are smaller, yes. Imagine turns as connected Cs. The short radius ones are smaller Cs.
Completing turns means you make a complete C, not a bunch of connected Ss. Does that make sense? For a completed turn, at the end of it you make your skis point across the hill at the trees. Or across the "fall line," if you want to sound like you're a ski instructor
. That part qualifies a turn as "completed."
Not completing turns makes you go fast. At the end of each incompleted turn your skis go diagonal, not horizontal, across the trail. They don't slow down much.
The end of the completed turn, no matter how short your across-the-slope travel is at that point, slows your downhill travel down. If you can get your skis to point the tiniest bit uphill as you complete them, then the skis won't take you very far across the trail. You'll have short C shaped turns.
This only works if you are not standing on the backs of your skis. The fronts must must must be pressed down onto the snow.
When a skier makes short radius turns that are completed, they can head straight down the hill in a narrow lane, not using up much left-right real estate with each turn. A narrow lane is usually called a narrow "corridor" because ski instructors want to avoid implying that ski trails have lanes like roads do.
Short radius turns in a narrow corridor are the golden nugget of skiing skill. Every turn then loses speed at its end, and it doesn't take up the whole trail putting you in danger of getting hit from behind.
I kept editing that post you just replied to as you were replying. It may have stuff in it you didn't get to read. I also kept editing this one
.