The difference between the trap and loading coil is this:

Loading coil "shortens" the radiator physical length by replacing the portion
of the radiator with inductance. Current on the ends of the coil is more-less
as it would be if there was a wire that coil replaces.

Trap typically resonates (by self resonance or with aid of parallel capacitor)
on the operating frequency of the portion of radiator between the feedpoint and
the the trap. It presents high impedance and practically isolates rest of the
radiator beyond the trap. On other frequencies (lower) it becomes loading coil
"connecting" the rest of the radiator and at the same time shortening its
physical length.

So the coil is a coil. In DC circuits behaves as flat earth believers want it
to behave in AC circuits. In RF curcuits, the current distribution depends on
the frequency and position of the coil along the radiator.

Check my web page for the start of the argument and some explanations
www.K3BU.us

Yuri, K3BU