Half jump terminology

[sampaguita]

Are the "half toe loop" and the "ballet jump" the same? Why the term "ballet jump"?

And why is the half loop not really a half jump? Is there a term for a jump that starts with a loop entrance but lands on the left toepick, going forward (similar to the half flip)?

[FigureSpins]

A Ballet jump takes off and lands on the same foot; a "half toe loop" takes off from one foot and lands on the other.
All toepicks, all the time.

If the skater uses a Loop BO edge to take off, then completes half a rotation and lands forward (toepick-opposite foot FI edge), it's a Falling Leaf jump.  If they perform a Split jump using that entrance/landing, it's a Split Falling Leaf jump.

Both the Loop and the Half Loop take off from a BO edge and land backwards, BO / BI, respectively.
They're both considered full-rotation jumps for the simple reason that they don't land forward after a backward takeoff.

[sampaguita]

Ah, thank you for that, FigureSpins! You answered all my questions. Happy New Year!