Both of course, the shape makes little difference - however, the upper one if intended for low frequencies (50Hz etc.), and the lower one for high frequencies (100KHz+?).
If you drop a magnet through them you will get a pulse - simple school physics.
If you put a wire through the coil with the square hole, you won't get much voltage, if any. You need the wires to be vaguely parallel to induce voltage.
If you put a wire through the coil with the square hole, you won't get much voltage, if any. You need the wires to be vaguely parallel to induce voltage.
2. In through-the-hole current sensors and current transformers, there is a magnetic core going around the hole, and the sensing wires also go through the hole. In the first picture in post #1, it is a coil designed to have a magnetic core going through the middle. It is possible to add a seconds winding, but that would also have to be around the core, not along the core.
Diver is spot on, no functional output from the first one, the second would work (as a current transformer, most likely).
Think of it as coupled windings - extra turns in common axis to existing ones, for both to share a magnetic field that follows the same path.
No commonality with the first square one, but there is with the toroid.