How does capacitive coupling work for measurements
Just because a wire is coiled around another wire, it doesn't mean it uses magnetic coupling as the principle for extracting a signal. To effectively utilize magnetic coupling you have to: -


Access both ends of the coiled wire electrically. I don't see any evidence of that in your lower diagram
A coil that wraps around a conductor's circumference will not receive an induced emf due to magnetic coupling because it is in the wrong orientation.


Almost certainly the wire is coiled around the conductor just to increase surface area "contact" through the insulator.

As to elaborating: -


  how capacitive coupling works in these two measurement setups?


You should explain your skill level and understanding of how capacitors work before I bore you with stuff you already know and waste my time and yours. If you are an absolute beginner then this means you should do some reasearch because this site isn't geared up for training like that.