Different currents at each end of a coil are easily explained.

A coil has capacitance to its surroundings distributed along its
length. And current flows from it radially.

Every coil has length. Both L and C are distributed. Therefore the
coil behaves as a transmission line. There are standing waves. Current
and voltage both vary with length.

The longer the line the greater the variation.

The line has phase-shift, Zo and attenuation resulting from wire loss
resistance and radiation resistance.

The line can have a resonant length. It then becomes a short antenna.

The whole business can be mathematically modelled.
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Reg, G4FGQ.